Internal problem ID [3705]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 980.
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 {y^{2} \left (y^{\prime }\right )^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +x^{2} a +\left (1-a \right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.446 (sec). Leaf size: 251
dsolve(y(x)^2*diff(y(x),x)^2+2*a*x*y(x)*diff(y(x),x)+(a-1)*b+a*x^2+(1-a)*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {-a \,x^{2}+b} \\ y \relax (x ) = -\sqrt {-a \,x^{2}+b} \\ y \relax (x ) = \frac {\sqrt {-a^{2} x^{2}-2 a \sqrt {-b \,a^{2}+c_{1} a^{2}+a b -c_{1} a}\, x +c_{1} a +b \,a^{2}-a b}}{a} \\ y \relax (x ) = \frac {\sqrt {-a^{2} x^{2}+2 a \sqrt {-b \,a^{2}+c_{1} a^{2}+a b -c_{1} a}\, x +c_{1} a +b \,a^{2}-a b}}{a} \\ y \relax (x ) = -\frac {\sqrt {-a^{2} x^{2}-2 a \sqrt {-b \,a^{2}+c_{1} a^{2}+a b -c_{1} a}\, x +c_{1} a +b \,a^{2}-a b}}{a} \\ y \relax (x ) = -\frac {\sqrt {-a^{2} x^{2}+2 a \sqrt {-b \,a^{2}+c_{1} a^{2}+a b -c_{1} a}\, x +c_{1} a +b \,a^{2}-a b}}{a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.145 (sec). Leaf size: 65
DSolve[y[x]^2 (y'[x])^2+2 a x y[x] y'[x]+(a-1)b+a x^2+(1-a)y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-2 (a-1) c_1 x+(a-1) c_1{}^2+b-x^2} \\ y(x)\to \sqrt {-2 (a-1) c_1 x+(a-1) c_1{}^2+b-x^2} \\ \end{align*}