Internal problem ID [4139]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22, problem 18, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -4 y-x^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2}}{x^{2}}+c_{1} x^{2}+\frac {x^{3}}{5} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 25
DSolve[x^2*y''[x]+x*y'[x]-4*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3}{5}+c_2 x^2+\frac {c_1}{x^2} \\ \end{align*}