# Solving differential equations with wolfram alpha [closed]

is there a way to solve this equation using wolfram alpha:

$$\frac{\partial u}{\partial t}-\frac{\partial ^2u}{\partial x^2}=0$$ and $$u(t,0)=u(t,\pi)=0$$, $$u(0,x)=2\sin(2x)-3\sin(3x)$$

Thanks all

• I’d seen it but still was having problem how to input my equation – user114138 Feb 23 at 16:58
• Is that the correct equation? Because I see no dependence on $t$ at all. Viewed only as a function of $x$, $u' = u"$ which has exponential solutions that can't satisfy the boundary conditions. – RobertTheTutor Feb 23 at 17:09
• I suspect it should be $$\frac{\partial u}{\partial t} - \frac{\partial^2 u}{\partial x^2} = 0$$ – Robert Israel Feb 23 at 17:19
• $u=2e^{-4t}\sin(2x)-3e^{-9t}\sin(3x)$. – JJacquelin Feb 23 at 18:27
• I was unable to get WolframAlpha to do it either (and I'm pretty good with both Mathematica and WolframAlpha). – Patrick Stevens Feb 23 at 18:59

Try the Wolfram command

DSolve[
{D[u[t,x], t]==D[u[t,x], {x,2}],
u[0,x]==2Sin[2 x]-3Sin[3 x],
u[t,0]==0, u[t,Pi]==0}, u, {{t,0,Infinity}, {x,0,Pi}}]


which returns

{{u->Function[{t,x},(2*E^(5*t)*Sin[2*x]- 3*Sin[3*x])/E^(9*t)]}}


You may still be able to get this somehow using Wolfram|Alpha but is it worth the effort?