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<blockquote data-quote="07sanjeewakaru" data-source="post: 16435452" data-attributes="member: 460140"><p><strong><strong><span style="font-size: 15px">(∂f(x,y))/∂x=Axy+Bx^2;</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Meka Anukalanaya karanawa x wishayen....Partial defferentiate karaddi aneth variable eka ganan ganne ne wage...Aneth paththata y ganan nogena Anukalanaya karanawa.......</span></strong></strong></p><p><strong><strong><span style="font-size: 15px"></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">f(x,y)=Ayx^2/2+Bx^3/3+f<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" /></span></strong></strong></p><p><strong><strong><span style="font-size: 15px"></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Habai Abimatha niyathaya y matha rada pawathinawa...Eka niyathaknewei..Ei f(x,y),x,y wala function ekakne....(<span style="color: DarkRed">nikan function ekak anukalanaya karama dana niyathe variable eka matha rada pawathinne ne wage thama....</span>)</span></strong></strong></p><p><strong><strong><span style="font-size: 15px"></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Dan meka y wishayen Patial differentiate karanawa.....Dan y witharai variable eka...</span></strong></strong></p><p><strong><strong><span style="font-size: 15px"></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">(∂f(x,y))/∂y=Ax^2/2+f '<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" />....(3)</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">f<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" /> kiyanne y wala function ekakne..eka y walin awakalanaya karama...f '<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" />..</span></strong></strong></p><p><strong><strong><span style="font-size: 15px"></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Dan meka (2) ta samana karanawa....</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Ax^2/2+f '<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" />=Cy^2+Dxy^2</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">f '<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" />=Cy^2+Dxy^2-Ax^2/2</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Meka onama x,y walata true wenne....</span></strong></strong></p><p><strong><strong><span style="font-size: 15px"><span style="color: DarkRed">A=0,.....(4)</span></span></strong></strong></p><p><strong><strong><span style="font-size: 15px"><span style="color: DarkRed">D=0......(5)</span></span></strong></strong></p><p><strong><strong><span style="font-size: 15px"><span style="color: DarkRed">(f '<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" /> only depend on y not x)</span></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">and....</span></strong></strong></p><p><strong><strong><span style="font-size: 15px"></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">f '<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" />=Cy^2...</span></strong></strong></p><p><strong><strong><span style="font-size: 15px"></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Dan meka normal differential equation ekak...Anukalaya karanta thiyenne...</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">f<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" />=Cy^3/3+k</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">k..Abimatha niyathe....</span></strong></strong></p><p><strong><strong><span style="font-size: 15px"></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">(3)n</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">f(x,y)=Ayx^2/2+Bx^3/3+f<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" /></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">(4)n,</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">A=0 ne..</span></strong></strong></p><p><strong><strong><span style="font-size: 15px"></span></strong></strong></p><p><strong><strong><span style="font-size: 15px"><span style="color: DarkRed">f(x,y)=Bx^3/3+Cy^3/3+k.....where k is a constant independent of x,y</span></span></strong></strong></p><p><strong><strong><span style="font-size: 15px"><span style="color: DarkRed"></span></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Oya mata therichcha hati....<img src="/styles/default/xenforo/smilies/default/happy.gif" class="smilie" loading="lazy" alt=":)" title="Happy :)" data-shortname=":)" /><img src="/styles/default/xenforo/smilies/default/happy.gif" class="smilie" loading="lazy" alt=":)" title="Happy :)" data-shortname=":)" /><img src="/styles/default/xenforo/smilies/default/happy.gif" class="smilie" loading="lazy" alt=":)" title="Happy :)" data-shortname=":)" /><img src="/styles/default/xenforo/smilies/default/happy.gif" class="smilie" loading="lazy" alt=":)" title="Happy :)" data-shortname=":)" /></span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Meka kohehari thibba ganakda..Neththan oya hithala damma ekakda....</span></strong></strong></p><p><strong><strong><span style="font-size: 15px">Kohomath hama A,B,C,D ekakatama f(x,y) hoyanta ba....<img src="/styles/default/xenforo/smilies/default/happy.gif" class="smilie" loading="lazy" alt=":)" title="Happy :)" data-shortname=":)" /><img src="/styles/default/xenforo/smilies/default/happy.gif" class="smilie" loading="lazy" alt=":)" title="Happy :)" data-shortname=":)" /><img src="/styles/default/xenforo/smilies/default/happy.gif" class="smilie" loading="lazy" alt=":)" title="Happy :)" data-shortname=":)" /></span></strong></strong></p></blockquote><p></p>
[QUOTE="07sanjeewakaru, post: 16435452, member: 460140"] [B][B][SIZE="4"](∂f(x,y))/∂x=Axy+Bx^2; Meka Anukalanaya karanawa x wishayen....Partial defferentiate karaddi aneth variable eka ganan ganne ne wage...Aneth paththata y ganan nogena Anukalanaya karanawa....... f(x,y)=Ayx^2/2+Bx^3/3+f(y) Habai Abimatha niyathaya y matha rada pawathinawa...Eka niyathaknewei..Ei f(x,y),x,y wala function ekakne....([COLOR="DarkRed"]nikan function ekak anukalanaya karama dana niyathe variable eka matha rada pawathinne ne wage thama....[/COLOR]) Dan meka y wishayen Patial differentiate karanawa.....Dan y witharai variable eka... (∂f(x,y))/∂y=Ax^2/2+f '(y)....(3) f(y) kiyanne y wala function ekakne..eka y walin awakalanaya karama...f '(y).. Dan meka (2) ta samana karanawa.... Ax^2/2+f '(y)=Cy^2+Dxy^2 f '(y)=Cy^2+Dxy^2-Ax^2/2 Meka onama x,y walata true wenne.... [COLOR="DarkRed"]A=0,.....(4) D=0......(5)[/COLOR] [COLOR="DarkRed"](f '(y) only depend on y not x)[/COLOR] and.... f '(y)=Cy^2... Dan meka normal differential equation ekak...Anukalaya karanta thiyenne... f(y)=Cy^3/3+k k..Abimatha niyathe.... (3)n f(x,y)=Ayx^2/2+Bx^3/3+f(y) (4)n, A=0 ne.. [COLOR="DarkRed"]f(x,y)=Bx^3/3+Cy^3/3+k.....where k is a constant independent of x,y [/COLOR] Oya mata therichcha hati....:):):):) Meka kohehari thibba ganakda..Neththan oya hithala damma ekakda.... Kohomath hama A,B,C,D ekakatama f(x,y) hoyanta ba....:):):)[/SIZE][/B][/B] [/QUOTE]
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