39.4.7 problem Problem 12.15

Internal problem ID [6541]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page 109
Problem number : Problem 12.15
Date solved : Monday, January 27, 2025 at 02:12:00 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }&=x^{3} {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 18

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

\[ y = \left (x -1\right ) {\mathrm e}^{x}+\frac {c_1 \,x^{2}}{2}+c_2 \]

✓ Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 24

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

\[ y(x)\to \frac {c_1 x^2}{2}+e^x (x-1)+c_2 \]