75.6.14 problem 138

Internal problem ID [16770]
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 : 138
Date solved : Tuesday, January 28, 2025 at 09:21:58 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+x y \,{\mathrm e}^{x}&={\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 20

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

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