#### 2.10.3 $$u_{tt} - u_{xx} - \frac{2}{x} u_x = 0$$ with $$u(x,0)=0,u_t(x,0)=g(x)$$

problem number 105

Problem 2.4.18 from Peter Olver, Intoduction to Partial diﬀerential equations, 4th edition.

Solve for $$u(x,t)$$ $u_{tt} - u_{xx} - \frac{2}{x} u_x = 0$

With $$u(x,0)=0,u_t(x,0)=g(x)$$. Note, in the book, it says to assume $$g(x)$$ is even function. In the code below, this assumption is not used. When I ﬁnd the correct way to implement this assumption in CAS, will have to re-run these.

Mathematica

Failed

Maple

$u \left ( x,t \right ) =\sum _{n=0}^{\infty }{\frac{{t}^{2\,n+1} \left ( U\mapsto 0^{ \left ( n \right ) } \right ) \left ( g \left ( x \right ) \right ) }{ \left ( 2\,n+1 \right ) !}}$