Internal problem ID [4689]
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]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x -x^{3} {\mathrm e}^{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{1} x^{2}}{2}+{\mathrm e}^{x} x -{\mathrm e}^{x}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.078 (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*}