75.1.13 problem 15

Internal problem ID [16676]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 09:17:44 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

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

\[ y = \frac {\left ({\mathrm e}^{3 x}+3 c_{1} \right ) {\mathrm e}^{-2 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 21

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

\[ y(x)\to \frac {e^x}{3}+c_1 e^{-2 x} \]