Internal problem ID [2946]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 198.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y-a \sqrt {y^{2}+b^{2} x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 41
dsolve(x*diff(y(x),x) = y(x)+a*sqrt(y(x)^2+b^2*x^2),y(x), singsol=all)
\[ \frac {x^{-a} y \relax (x )}{x}+\frac {x^{-a} \sqrt {y \relax (x )^{2}+b^{2} x^{2}}}{x}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.415 (sec). Leaf size: 73
DSolve[x y'[x]==y[x]+a Sqrt[y[x]^2+b^2 x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} b e^{-c_1} \left (x^{1-a}-e^{2 c_1} x^{a+1}\right ) \\ y(x)\to \frac {1}{2} b e^{-c_1} x^{1-a} \left (-1+e^{2 c_1} x^{2 a}\right ) \\ \end{align*}