Internal problem ID [948]
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: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+x^{2} \left (1+y\right ) \left (y-2\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 35
dsolve(diff(y(x),x)+x^2*(y(x)+1)*(y(x)-2)^2=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (3 x^{3} {\mathrm e}^{\textit {\_Z}}+\ln \left ({\mathrm e}^{\textit {\_Z}}+3\right ) {\mathrm e}^{\textit {\_Z}}+9 c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-3\right )}+2 \]
✓ Solution by Mathematica
Time used: 0.548 (sec). Leaf size: 52
DSolve[y'[x]+x^2*(y[x]+1)*(y[x]-2)^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{9} \left (-\frac {3}{\text {$\#$1}-2}-\log (\text {$\#$1}-2)+\log (\text {$\#$1}+1)\right )\&\right ]\left [-\frac {x^3}{3}+c_1\right ] \\ y(x)\to -1 \\ y(x)\to 2 \\ \end{align*}