Internal problem ID [15040]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+y x \,{\mathrm e}^{x}={\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)+x*y(x)*exp(x)=exp( (1-x)*exp(x) ),y(x), singsol=all)
\[ y \left (x \right ) = \left (x +c_{1} \right ) {\mathrm e}^{-\left (-1+x \right ) {\mathrm e}^{x}} \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 20
DSolve[y'[x]+x*y[x]*Exp[x]==Exp[ (1-x)*Exp[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-e^x (x-1)} (x+c_1) \]