Internal problem ID [6311]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y}{3}-\frac {\left (1-2 x \right ) y^{4}}{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 83
dsolve(diff(y(x),x)+y(x)/3= (1-2*x)/3*y(x)^4,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\left (c_{1} {\mathrm e}^{x}-2 x -1\right )^{\frac {1}{3}}} \\ y \relax (x ) = -\frac {1}{2 \left (c_{1} {\mathrm e}^{x}-2 x -1\right )^{\frac {1}{3}}}-\frac {i \sqrt {3}}{2 \left (c_{1} {\mathrm e}^{x}-2 x -1\right )^{\frac {1}{3}}} \\ y \relax (x ) = -\frac {1}{2 \left (c_{1} {\mathrm e}^{x}-2 x -1\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}}{2 \left (c_{1} {\mathrm e}^{x}-2 x -1\right )^{\frac {1}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.37 (sec). Leaf size: 76
DSolve[y'[x]+y[x]/3== (1-2*x)/3*y[x]^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\sqrt [3]{-2 x+c_1 e^x-1}} \\ y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{-2 x+c_1 e^x-1}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{-2 x+c_1 e^x-1}} \\ y(x)\to 0 \\ \end{align*}