if $u(x,y) $ satisfies $u_{xx} + u_{yy} = 0$ then $v=u(\frac{x}{x^2+y^2},\frac{y}{x^2+y^2})$ satisfies $v_{xx} + v_{yy} = 0$
87390
Laplace equation of composite function
152293
Solution of $y''+xy=0$
88311
Linear functional f(v)=0 imply v=0
15025
Solve $xu_x+(x+y)u_y=1$ when $u(1,y)=y$
49211
Solving $f(x+y) = f(x)f(y)f(xy)$
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
8711
Problems in the relation $a=v\frac{\mathrm{d}v}{\mathrm{d}x}$
49044
Question about Eulers formula $v - e + f = 2$
63410
Proof on showing if F(x,y,z)=0 then product of partial derivatives (evaluated at an assigned coordinate) is -1
11707
If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$
51483
Prove: If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
82365
what should be the range of $u$ satisfying following equation.
101112
Transport equation $u_t + xu_x + u = 0$ with $u(x_0, 0) = \cos(x_0)$
35564
Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$
55364
Show $au_x+bu_y=f(x,y)$ gives $u(x,y)=(a^2+b^2)^{-\frac{1}{2}}\int_{L}fds +g(bx-ay)$ if $a\neq 0$.
133545
$y(x)$ be a continuous solution of the initial value problem $y'+2y=f(x)$ , $y(0)=0$
9143
Solve $u_{xx}-3u_{xt}-4u_{tt}=0$ where $u(x,0)=x^2$ and $u_t(x,0)=e^x$