56.1.20 problem 20

Internal problem ID [8732]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 20
Date solved : Monday, January 27, 2025 at 04:45:09 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+\frac {y}{3}&=\frac {\left (1-2 x \right ) y^{4}}{3} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 61

dsolve(diff(y(x),x)+y(x)/3= (1-2*x)/3*y(x)^4,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\left ({\mathrm e}^{x} c_{1} -2 x -1\right )^{{1}/{3}}} \\ y &= -\frac {1+i \sqrt {3}}{2 \left ({\mathrm e}^{x} c_{1} -2 x -1\right )^{{1}/{3}}} \\ y &= \frac {i \sqrt {3}-1}{2 \left ({\mathrm e}^{x} c_{1} -2 x -1\right )^{{1}/{3}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 5.413 (sec). Leaf size: 76

DSolve[D[y[x],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*}