Internal problem ID [252]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 57.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -y-72 x^{5}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=72*x^5,y(x), singsol=all)
\[ y \relax (x ) = c_{2} x +3 x^{5}+\frac {c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 21
DSolve[x^2*y''[x]+x*y'[x]-y[x]==72*x^5,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 x^5+c_2 x+\frac {c_1}{x} \\ \end{align*}