Internal problem ID [3957]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _Bernoulli]
Solve \begin {gather*} \boxed {{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left ({\mathrm e}^{x} x -6\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 38
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)
\[ y \relax (x ) = \frac {\left (-1+i \sqrt {3}\right ) \left (-\left ({\mathrm e}^{x}+5\right ) \left (x \,{\mathrm e}^{x}-6\right )^{2}\right )^{\frac {1}{3}}}{2 x \,{\mathrm e}^{x}-12} \]
✓ Solution by Mathematica
Time used: 1.148 (sec). Leaf size: 28
DSolve[{Exp[x]*(y[x]^3+x*y[x]^3+1)+3*y[x]^2*(x*Exp[x]-6)*y'[x]==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{-e^x-5}}{\sqrt [3]{e^x x-6}} \\ \end{align*}