32.3.11 problem Exact Differential equations. Exercise 9.15, page 79

Internal problem ID [5809]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number : Exact Differential equations. Exercise 9.15, page 79
Date solved : Monday, January 27, 2025 at 01:19:50 PM
CAS classification : [_exact, _Bernoulli]

\begin{align*} {\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.163 (sec). Leaf size: 37

dsolve([exp(x)*(y(x)^3+x*y(x)^3+1)+3*y(x)^2*(x*exp(x)-6)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (i \sqrt {3}-1\right ) {\left (-\left ({\mathrm e}^{x}+5\right ) \left (x \,{\mathrm e}^{x}-6\right )^{2}\right )}^{{1}/{3}}}{2 x \,{\mathrm e}^{x}-12} \]

✓ Solution by Mathematica

Time used: 1.281 (sec). Leaf size: 28

DSolve[{Exp[x]*(y[x]^3+x*y[x]^3+1)+3*y[x]^2*(x*Exp[x]-6)*D[y[x],x]==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt [3]{-e^x-5}}{\sqrt [3]{e^x x-6}} \]