Internal problem ID [4213]
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)]`]]
\[ \boxed {y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (1-a \right ) y^{2}=-\left (a -1\right ) b -a \,x^{2}} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 93
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 \left (x \right ) = \sqrt {-a \,x^{2}+b} y \left (x \right ) = -\sqrt {-a \,x^{2}+b} y \left (x \right ) = \sqrt {c_{1}^{2} a -2 a c_{1} x -c_{1}^{2}+2 c_{1} x -x^{2}+b} y \left (x \right ) = -\sqrt {c_{1}^{2} a -2 a c_{1} x -c_{1}^{2}+2 c_{1} x -x^{2}+b} \end{align*}
✓ Solution by Mathematica
Time used: 1.186 (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*}