40.9.8 problem 18

Internal problem ID [6718]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:24:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-y(x)=4*x*exp(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]-y[x]==4*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

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