Internal problem ID [7951]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 371.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-y^{3}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.264 (sec). Leaf size: 24
dsolve(diff(y(x),x)^2-y(x)^3+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 1 \\ y \relax (x ) = 0 \\ y \relax (x ) = \tan ^{2}\left (\frac {c_{1}}{2}-\frac {x}{2}\right )+1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.518 (sec). Leaf size: 43
DSolve[y[x]^2 - y[x]^3 + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sec ^2\left (\frac {x-c_1}{2}\right ) \\ y(x)\to \sec ^2\left (\frac {x+c_1}{2}\right ) \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}