Internal problem ID [936]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y-1\right )^{2} y^{\prime }-2 x -3=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 102
dsolve((y(x)-1)^2*diff(y(x),x)=2*x+3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (3 x^{2}+9 x +3 c_{1}\right )^{\frac {1}{3}}+1 \\ y \relax (x ) = -\frac {\left (3 x^{2}+9 x +3 c_{1}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (3 x^{2}+9 x +3 c_{1}\right )^{\frac {1}{3}}}{2}+1 \\ y \relax (x ) = -\frac {\left (3 x^{2}+9 x +3 c_{1}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (3 x^{2}+9 x +3 c_{1}\right )^{\frac {1}{3}}}{2}+1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.465 (sec). Leaf size: 97
DSolve[(y[x]-1)^2*y'[x]==2*x+3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+\sqrt [3]{3 x (x+3)-1+3 c_1} \\ y(x)\to 1+\frac {1}{2} i \left (\sqrt {3}+i\right ) \sqrt [3]{3 x (x+3)-1+3 c_1} \\ y(x)\to 1+\frac {1}{2} \left (-1-i \sqrt {3}\right ) \sqrt [3]{3 x (x+3)-1+3 c_1} \\ \end{align*}