Internal problem ID [3722]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 34
Problem number: 998.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {\left (a -b \right ) y^{2} \left (y^{\prime }\right )^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.179 (sec). Leaf size: 260
dsolve((a-b)*y(x)^2*diff(y(x),x)^2-2*b*x*y(x)*diff(y(x),x)-a*b-b*x^2+a*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (a -b \right ) b \left (x^{2}+a -b \right )}}{a -b} \\ y \relax (x ) = -\frac {\sqrt {\left (a -b \right ) b \left (x^{2}+a -b \right )}}{a -b} \\ y \relax (x ) = \frac {\sqrt {-c_{1} a b +c_{1} b^{2}-b^{2} x^{2}-2 b \sqrt {-a \,b^{2}+c_{1} a b}\, x +a \,b^{2}}}{b} \\ y \relax (x ) = \frac {\sqrt {-c_{1} a b +c_{1} b^{2}-b^{2} x^{2}+2 b \sqrt {-a \,b^{2}+c_{1} a b}\, x +a \,b^{2}}}{b} \\ y \relax (x ) = -\frac {\sqrt {-c_{1} a b +c_{1} b^{2}-b^{2} x^{2}-2 b \sqrt {-a \,b^{2}+c_{1} a b}\, x +a \,b^{2}}}{b} \\ y \relax (x ) = -\frac {\sqrt {-c_{1} a b +c_{1} b^{2}-b^{2} x^{2}+2 b \sqrt {-a \,b^{2}+c_{1} a b}\, x +a \,b^{2}}}{b} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.39 (sec). Leaf size: 86
DSolve[(a-b) y[x]^2 (y'[x])^2 -2 b x y[x] y'[x]-a b -b x^2+a y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {b \left (b-x^2\right )+a \left (-b+(x-c_1){}^2\right )}}{\sqrt {b-a}} \\ y(x)\to \frac {\sqrt {b \left (b-x^2\right )+a \left (-b+(x-c_1){}^2\right )}}{\sqrt {b-a}} \\ \end{align*}