Internal problem ID [104]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
Solve \begin {gather*} \boxed {y^{3}+3 y^{2} y^{\prime }-{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 99
dsolve(y(x)^3+3*y(x)^2*diff(y(x),x) = exp(-x),y(x), singsol=all)
\begin{align*} y \relax (x ) = {\mathrm e}^{-x} \left (\left (c_{1}+x \right ) {\mathrm e}^{2 x}\right )^{\frac {1}{3}} \\ y \relax (x ) = -\frac {{\mathrm e}^{-x} \left (\left (c_{1}+x \right ) {\mathrm e}^{2 x}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, {\mathrm e}^{-x} \left (\left (c_{1}+x \right ) {\mathrm e}^{2 x}\right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {{\mathrm e}^{-x} \left (\left (c_{1}+x \right ) {\mathrm e}^{2 x}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, {\mathrm e}^{-x} \left (\left (c_{1}+x \right ) {\mathrm e}^{2 x}\right )^{\frac {1}{3}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.31 (sec). Leaf size: 72
DSolve[y[x]^3+3*y[x]^2*y'[x] == Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x/3} \sqrt [3]{x+c_1} \\ y(x)\to -\sqrt [3]{-1} e^{-x/3} \sqrt [3]{x+c_1} \\ y(x)\to (-1)^{2/3} e^{-x/3} \sqrt [3]{x+c_1} \\ \end{align*}