Internal problem ID [4158]
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]
\[ \boxed {\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}=-b} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 90
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 \left (x \right ) = \frac {\sqrt {-a^{2} b -b \,x^{2}}}{a} y \left (x \right ) = -\frac {\sqrt {-a^{2} b -b \,x^{2}}}{a} y \left (x \right ) = c_{1} x -\sqrt {-a^{2} c_{1}^{2}-b} y \left (x \right ) = c_{1} x +\sqrt {-a^{2} c_{1}^{2}-b} \end{align*}
✓ Solution by Mathematica
Time used: 0.463 (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*}