Internal problem ID [2088]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }-y^{\prime } x +y-9 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=9*x^2,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x}\, c_{2}+x c_{1}+3 x^{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 23
DSolve[2*x^2*y''[x]-x*y'[x]+y[x]==9*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 x^2+c_2 x+c_1 \sqrt {x} \\ \end{align*}