Answer to Question #178214 in Differential Equations for Lucy Buche Shehi

Question #178214

Find the integral surface of quasi linear partial differential equation xzp+yzq=-xy which passes through the curve y=x²,z=x³



1
Expert's answer
2021-04-13T23:42:58-0400

xzp+yzq=xyThis is lagrange’s equationPp+Qq=Rdxp=dyQ=dzxydxxz=dyyz    dxx=dyy    dxx=dyyInx=Iny+Ina    Inxy=Inaxy=aydx+xdy2zdzxyz+xyz2xyz=ydx+xdy2zdz0d(xy)2zdz=0xyz2=bψ(xy,xyz2)=0.xzp+yzq=-xy \\ \text{This is lagrange's equation}\\ Pp+Qq=R\\ \frac{dx}{p}=\frac{dy}{Q}=\frac{dz}{-xy}\\ \frac{dx}{xz}=\frac{dy}{yz} \implies \frac{dx}{x}=\frac{dy}{y}\\ \implies\int\frac{dx}{x}=\int\frac{dy}{y}\\ Inx=Iny+Ina\\ \implies In\frac{x}{y}=Ina\\ \frac{x}{y}=a\\ \frac{ydx+xdy-2zdz}{xyz+xyz-2xyz}=\frac{ydx+xdy-2zdz}{0}\\ d(xy)-2zdz=0\\ xy-z^2=b\\ \psi(\frac{x}{y},xy-z^2)=0.


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Comments

Assignment Expert
09.04.21, 21:21

Dear visitors, we have not solved this question yet.

Lucy Buche Shehi
07.04.21, 15:29

Have been waiting for the answer and it's giving me answer in progress

Nyabuto priscah
05.04.21, 12:33

An answer to question above under pde

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