Internal problem ID [10564]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number: 6(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+2 y-6 \,{\mathrm e}^{x}-4 x \,{\mathrm e}^{-2 x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x)+2*y(x)=6*exp(x)+4*x*exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (2 x^{2}+2 \,{\mathrm e}^{3 x}+c_{1} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 25
DSolve[y'[x]+2*y[x]==6*Exp[x]+4*x*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 e^x+e^{-2 x} \left (2 x^2+c_1\right ) \\ \end{align*}