Internal problem ID [4690]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page
109
Problem number: Problem 12.15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-x y^{\prime }-{\mathrm e}^{x} x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)=x^3*exp(x),y(x), singsol=all)
\[ y \relax (x ) = x \,{\mathrm e}^{x}-{\mathrm e}^{x}+\frac {c_{1} x^{2}}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.096 (sec). Leaf size: 24
DSolve[x^2*y''[x]-x*y'[x]==x^3*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 x^2}{2}+e^x (x-1)+c_2 \\ \end{align*}