Internal problem ID [8707]
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]
\[ \boxed {{y^{\prime }}^{2}-y^{3}+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 22
dsolve(diff(y(x),x)^2-y(x)^3+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 1 \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \sec \left (-\frac {x}{2}+\frac {c_{1}}{2}\right )^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.066 (sec). Leaf size: 45
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 1+\tan ^2\left (\frac {x+c_1}{2}\right ) \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}