60.1.370 problem 371

Internal problem ID [10384]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 371
Date solved : Monday, January 27, 2025 at 07:38:40 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-y^{3}+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 22

dsolve(diff(y(x),x)^2-y(x)^3+y(x)^2 = 0,y(x), singsol=all)
 

\begin{align*} y &= 1 \\ y &= 0 \\ y &= \sec \left (-\frac {x}{2}+\frac {c_{1}}{2}\right )^{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.090 (sec). Leaf size: 45

DSolve[y[x]^2 - y[x]^3 + D[y[x],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*}