Internal problem ID [15052]
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: 159.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime }=3 x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve((x^3+exp(y(x)))*diff(y(x),x)=3*x^2,y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (\frac {x^{3}}{\operatorname {LambertW}\left (\frac {x^{3}}{c_{1}}\right )}\right ) \]
✓ Solution by Mathematica
Time used: 3.536 (sec). Leaf size: 19
DSolve[(x^3+Exp[y[x]])*y'[x]==3*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to W\left (e^{-c_1} x^3\right )+c_1 \]