75.6.34 problem 167

Internal problem ID [16790]
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 : 167
Date solved : Tuesday, January 28, 2025 at 08:26:16 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 0.078 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.376 (sec). Leaf size: 15

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

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