74.4.65 problem 61 (b)

Internal problem ID [15958]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 61 (b)
Date solved : Tuesday, January 28, 2025 at 08:24:45 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 116

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

\begin{align*} y &= \frac {3^{{1}/{3}} \left (-\left (x +c_{1} \right )^{2}\right )^{{1}/{3}}-3 c_{1} -3 x}{9 x +9 c_{1}} \\ y &= \frac {\left (-i 3^{{5}/{6}}-3^{{1}/{3}}\right ) \left (-\left (x +c_{1} \right )^{2}\right )^{{1}/{3}}-6 x -6 c_{1}}{18 x +18 c_{1}} \\ y &= \frac {\left (i 3^{{5}/{6}}-3^{{1}/{3}}\right ) \left (-\left (x +c_{1} \right )^{2}\right )^{{1}/{3}}-6 x -6 c_{1}}{18 x +18 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.916 (sec). Leaf size: 144

DSolve[D[y[x],x]==(3*y[x]+1)^4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {3 x+\sqrt [3]{3} \sqrt [3]{(x+c_1){}^2}+3 c_1}{9 (x+c_1)} \\ y(x)\to \frac {-6 x+\sqrt [3]{3} \left (1-i \sqrt {3}\right ) \sqrt [3]{(x+c_1){}^2}-6 c_1}{18 (x+c_1)} \\ y(x)\to \frac {-6 x+\sqrt [3]{3} \left (1+i \sqrt {3}\right ) \sqrt [3]{(x+c_1){}^2}-6 c_1}{18 (x+c_1)} \\ y(x)\to -\frac {1}{3} \\ \end{align*}