64.12.22 problem 22

Internal problem ID [13526]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 05:51:54 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)-x*(x+2)*diff(y(x),x)+(x+2)*y(x)=x^3,y(x), singsol=all)
 

\[ y = x \left (-x +{\mathrm e}^{x} c_{1} +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 25

DSolve[x^2*D[y[x],{x,2}]-x*(x+2)*D[y[x],x]+(x+2)*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \left (x-c_2 e^{x+1}+1-e c_1\right ) \]