Internal problem ID [3454]
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]
\[ \boxed {x y^{\prime }-y-a \sqrt {y^{2}+b^{2} x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(x*diff(y(x),x) = y(x)+a*sqrt(y(x)^2+b^2*x^2),y(x), singsol=all)
\[ x^{-1-a} y \left (x \right )+x^{-1-a} \sqrt {y \left (x \right )^{2}+b^{2} x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.402 (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*}