Internal problem ID [7647]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 66.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\sqrt {{| y \left (y-1\right ) \left (-1+a y\right )|}}}{\sqrt {{| x \left (-1+x \right ) \left (x a -1\right )|}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 40
dsolve(diff(y(x),x) - sqrt(abs(y(x)*(1-y(x))*(1-a*y(x))))/sqrt(abs(x*(1-x)*(1-a*x)))=0,y(x), singsol=all)
\[ \int \frac {1}{\sqrt {{| x \left (x -1\right ) \left (a x -1\right )|}}}d x -\left (\int _{}^{y \relax (x )}\frac {1}{\sqrt {{| \textit {\_a} \left (-1+\textit {\_a} \right ) \left (a \textit {\_a} -1\right )|}}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.392 (sec). Leaf size: 81
DSolve[y'[x] - Sqrt[Abs[y[x]*(1-y[x])*(1-a*y[x])]]/Sqrt[Abs[x*(1-x)*(1-a*x)]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\sqrt {| (1-K[1]) K[1] (1-a K[1])| }}dK[1]\&\right ]\left [\int _1^x\frac {1}{\sqrt {| (K[2]-1) K[2] (a K[2]-1)| }}dK[2]+c_1\right ] \\ y(x)\to 0 \\ y(x)\to 1 \\ y(x)\to \frac {1}{a} \\ \end{align*}