39.2.7 problem Problem 11.50

Internal problem ID [6524]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary Problems. page 101
Problem number : Problem 11.50
Date solved : Monday, January 27, 2025 at 02:11:28 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x)-y(x)=x*exp(2*x)+1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 22

DSolve[D[y[x],x]-y[x]==x*Exp[2*x]+1,y[x],x,IncludeSingularSolutions -> True]
 

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