Internal problem ID [4672]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-y-{\mathrm e}^{2 x} x -1=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(y(x),x)-y(x)=x*exp(2*x)+1,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} x -{\mathrm e}^{2 x}-1+{\mathrm e}^{x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 21
DSolve[y'[x]-y[x]==x*Exp[2*x]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+e^x \left (e^x (x-1)+c_1\right ) \\ \end{align*}