29.26.25 problem 761

Internal problem ID [5346]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 761
Date solved : Monday, January 27, 2025 at 11:16:03 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=\left (y-1\right ) y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.039 (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: 1.066 (sec). Leaf size: 45

DSolve[(D[y[x],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*}