Solving $au_x + bu_y = f(x,y)$
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 $a\neq 0$.
142436
Solving a PDE with variable coefficients
105497
A function satisfying a series equation
25730
Solve $u_x + u_y + u = e^{x+2y}$
42699
Solve for $f(x)$ if $f(f(x))=6x-f(x)$
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 $u_t(x,0)=e^x$
106038
Burgers' equation $u_y + uu_x = 0$ with $u(x,0)=-x$
62529
Solve $y’ = \frac{2-xy^3}{3x^2y^2}$ using Bernoulli form
27127
Calculating $\iint (x+y) \, dx \, dy$
73519
Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
152293
Solution of $y''+xy=0$
32599
Solution to the functional equation $f(x^y)=f(x)^{f(y)}$
31732
If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
106033
Solve the system in $\mathbb{R}$