75.6.26 problem 159

Internal problem ID [16782]
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
Date solved : Tuesday, January 28, 2025 at 09:22:34 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} \left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime }&=3 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 19

dsolve((x^3+exp(y(x)))*diff(y(x),x)=3*x^2,y(x), singsol=all)
 

\[ y = \ln \left (\frac {x^{3}}{\operatorname {LambertW}\left (\frac {x^{3}}{c_{1}}\right )}\right ) \]

✓ Solution by Mathematica

Time used: 3.816 (sec). Leaf size: 19

DSolve[(x^3+Exp[y[x]])*D[y[x],x]==3*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to W\left (e^{-c_1} x^3\right )+c_1 \]