Internal problem ID [2597]
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]]
\[ \boxed {2 x^{2} y^{\prime \prime }-x y^{\prime }+y=9 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{2} x +c_{1} \sqrt {x}+3 x^{2} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 23
DSolve[2*x^2*y''[x]-x*y'[x]+y[x]==9*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x^2+c_2 x+c_1 \sqrt {x} \]