Internal problem ID [14734]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y=2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-6*y(x)=2*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2}}{x^{3}}+c_{1} x^{2}-\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 23
DSolve[x^2*y''[x]+2*x*y'[x]-6*y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{x^3}+c_2 x^2-\frac {x}{2} \]