Internal problem ID [5580]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF
PARAMETERS. Page 71
Problem number: 5(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y-x \left (1+x \right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve((x^2+x)*diff(y(x),x$2)+(2-x^2)*diff(y(x),x)-(2+x)*y(x)=x*(x+1)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{2}}{x}+c_{1} {\mathrm e}^{x}-\frac {x^{2}}{3}-x -1 \]
✓ Solution by Mathematica
Time used: 0.096 (sec). Leaf size: 45
DSolve[(x^2+x)*y''[x]+(2-x^2)*y'[x]-(2+x)*y[x]==x*(x+1)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{3}-x+\sqrt {2} c_2 e^{x+\frac {1}{2}}+\frac {c_1}{\sqrt {2 e} x}-1 \\ \end{align*}