75.6.13 problem 137

Internal problem ID [16769]
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 : 137
Date solved : Tuesday, January 28, 2025 at 09:21:56 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 17

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

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