Internal problem ID [3650]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 922.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
Solve \begin {gather*} \boxed {\left (a^{2}+x^{2}\right ) \left (y^{\prime }\right )^{2}-2 y^{\prime } y x +b +y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 59
dsolve((a^2+x^2)*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+b+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x -\sqrt {-a^{2} c_{1}^{2}-b} \\ y \relax (x ) = c_{1} x +\sqrt {-a^{2} c_{1}^{2}-b} \\ y \relax (x ) = \sqrt {a^{2}+x^{2}}\, c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.253 (sec). Leaf size: 100
DSolve[(a^2+x^2) (y'[x])^2-2 x y[x] y'[x]+b+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\sqrt {-b-a^2 c_1{}^2} \\ y(x)\to \sqrt {-b-a^2 c_1{}^2}+c_1 x \\ y(x)\to -\frac {\sqrt {-b \left (a^2+x^2\right )}}{a} \\ y(x)\to \frac {\sqrt {-b \left (a^2+x^2\right )}}{a} \\ \end{align*}