75.6.1 problem 125

Internal problem ID [16757]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 125
Date solved : Tuesday, January 28, 2025 at 09:21:23 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 17

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

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