Problem 5
The particular integral of \(\left(D^{2}+D D\right) z=\sin (x+y)\) is .
Problem 10
The order of the partial differential equation obtained by eliminating \(f\) from \(z=f\left(x^{2}+y^{2}\right)\), is ......
Problem 21
The partial differential equation from \(z=(c+x)^{2}+y\) is (i) \(z=\left(\frac{d e}{\partial x}\right)^{2}+y\) \((j) z=\left(\frac{\partial z}{\partial y}\right)^{2}+y\) \((i a) z=\frac{1}{4}\left(\frac{\partial z}{\partial x}\right)^{2}+y\) (iw) \(z=\frac{1}{4}\left(\frac{\partial e}{\partial y}\right)^{2}+y_{.}\)
Problem 28
\(x u,+u_{m}=0\) is a non-linear partial differential equation.
Problem 30
\(u=e^{-1} \sin x\) is a solution of \(\frac{\partial^{2} u}{\partial t^{2}}+\frac{\partial^{2} u}{d x^{2}}=0\).
