Internal problem ID [254]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 59.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=x^4,y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+\ln \relax (x ) c_{1} x^{2}+\frac {x^{4}}{4} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 26
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x^2 \left (x^2+8 c_2 \log (x)+4 c_1\right ) \\ \end{align*}