Internal problem ID [14223]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\left (3 y+1\right )^{4}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 118
dsolve(diff(y(x),x)=(3*y(x)+1)^4,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {3^{\frac {1}{3}} \left (-\left (c_{1} +x \right )^{2}\right )^{\frac {1}{3}}-3 c_{1} -3 x}{9 c_{1} +9 x} \\ y \left (x \right ) &= \frac {\left (-i 3^{\frac {5}{6}}-3^{\frac {1}{3}}\right ) \left (-\left (c_{1} +x \right )^{2}\right )^{\frac {1}{3}}-6 x -6 c_{1}}{18 c_{1} +18 x} \\ y \left (x \right ) &= \frac {\left (i 3^{\frac {5}{6}}-3^{\frac {1}{3}}\right ) \left (-\left (c_{1} +x \right )^{2}\right )^{\frac {1}{3}}-6 x -6 c_{1}}{18 c_{1} +18 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.928 (sec). Leaf size: 144
DSolve[y'[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*}