39.1.12 problem Problem 11.14

Internal problem ID [6517]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.14
Date solved : Monday, January 27, 2025 at 02:11:15 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 34

dsolve(diff(y(x),x)-5*y(x)=x^2*exp(x)-x*exp(5*x),y(x), singsol=all)
 

\[ y = -\frac {\left (x^{2}-2 c_1 \right ) {\mathrm e}^{x} {\mathrm e}^{4 x}}{2}+\frac {\left (-8 x^{2}-4 x -1\right ) {\mathrm e}^{x}}{32} \]

✓ Solution by Mathematica

Time used: 0.342 (sec). Leaf size: 39

DSolve[D[y[x],x]-5*y[x]==x^2*Exp[x]-x*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{32} e^x \left (8 x^2+4 x+1\right )+e^{5 x} \left (-\frac {x^2}{2}+c_1\right ) \]