Internal problem ID [15060]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-y \left ({\mathrm e}^{x}+\ln \left (y\right )\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve(diff(y(x),x)=y(x)*(exp(x)+ln(y(x))),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{{\mathrm e}^{x} \left (x +c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 0.372 (sec). Leaf size: 15
DSolve[y'[x]==y[x]*(Exp[x]+Log[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{e^x (x+c_1)} \]