Internal problem ID [3495]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 762.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\left (y-a \right ) \left (y-b \right ) \left (y-c \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.131 (sec). Leaf size: 79
dsolve(diff(y(x),x)^2 = (y(x)-a)*(y(x)-b)*(y(x)-c),y(x), singsol=all)
\begin{align*} y \relax (x ) = a \\ y \relax (x ) = b \\ y \relax (x ) = c \\ x -\left (\int _{}^{y \relax (x )}\frac {1}{\sqrt {\left (\textit {\_a} -a \right ) \left (\textit {\_a} -b \right ) \left (\textit {\_a} -c \right )}}d \textit {\_a} \right )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}-\frac {1}{\sqrt {\left (\textit {\_a} -a \right ) \left (\textit {\_a} -b \right ) \left (\textit {\_a} -c \right )}}d \textit {\_a} \right )-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 173
DSolve[(y'[x])^2==(y[x]-a)(y[x]-b)(y[x]-c),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ns}\left (\frac {1}{2} \sqrt {a-b} (c_1-i x)|\frac {a-c}{a-b}\right ){}^2 \left (a \text {sn}\left (\frac {1}{2} \sqrt {a-b} (c_1-i x)|\frac {a-c}{a-b}\right ){}^2-a+b\right ) \\ y(x)\to \text {ns}\left (\frac {1}{2} \sqrt {a-b} (i x+c_1)|\frac {a-c}{a-b}\right ){}^2 \left (a \text {sn}\left (\frac {1}{2} \sqrt {a-b} (i x+c_1)|\frac {a-c}{a-b}\right ){}^2-a+b\right ) \\ \end{align*}