Internal problem ID [2311]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.9, Reduction of Order. page
572
Problem number: Problem 12.
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-8 x^{4}=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 22
dsolve([x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=8*x^4,x^2],y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+\ln \relax (x ) c_{1} x^{2}+2 x^{4} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 23
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==8*x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (2 x^2+2 c_2 \log (x)+c_1\right ) \\ \end{align*}