Internal problem ID [4002]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 761.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-\left (y-1\right ) y^{2}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 22
dsolve(diff(y(x),x)^2 = (y(x)-1)*y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 1 \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \sec \left (\frac {c_{1}}{2}-\frac {x}{2}\right )^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.652 (sec). Leaf size: 45
DSolve[(y'[x])^2==(y[x]-1)y[x]^2,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*}