ODE
\[ x^2 y''(x)-\left (2-x^2\right ) y(x)=x^4 \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.228796 (sec), leaf count = 53
\[\left \{\left \{y(x)\to \frac {x^3-\sqrt {\frac {2}{\pi }} (c_1 x+c_2) \cos (x)+\sqrt {\frac {2}{\pi }} (c_1-c_2 x) \sin (x)}{x}\right \}\right \}\]
Maple ✓
cpu = 0.221 (sec), leaf count = 34
\[\left [y \left (x \right ) = \frac {\left (x \cos \left (x \right )-\sin \left (x \right )\right ) \textit {\_C2}}{x}+\frac {\left (\cos \left (x \right )+x \sin \left (x \right )\right ) \textit {\_C1}}{x}+x^{2}\right ]\] Mathematica raw input
DSolve[-((2 - x^2)*y[x]) + x^2*y''[x] == x^4,y[x],x]
Mathematica raw output
{{y[x] -> (x^3 - Sqrt[2/Pi]*(x*C[1] + C[2])*Cos[x] + Sqrt[2/Pi]*(C[1] - x*C[2])*Sin[x])/x}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-(-x^2+2)*y(x) = x^4, y(x))
Maple raw output
[y(x) = 1/x*(x*cos(x)-sin(x))*_C2+1/x*(cos(x)+x*sin(x))*_C1+x^2]