Internal problem ID [8116]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 536.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (-a^{2}+x^{2}\right ) \left (y^{\prime }\right )^{3}+b x \left (-a^{2}+x^{2}\right ) \left (y^{\prime }\right )^{2}+y^{\prime }+b x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 52
dsolve((-a^2+x^2)*diff(y(x),x)^3+b*x*(-a^2+x^2)*diff(y(x),x)^2+diff(y(x),x)+b*x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {b \,x^{2}}{2}+c_{1} \\ y \relax (x ) = \arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+c_{1} \\ y \relax (x ) = -\arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 64
DSolve[b*x + y'[x] + b*x*(-a^2 + x^2)*y'[x]^2 + (-a^2 + x^2)*y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {b x^2}{2}+c_1 \\ y(x)\to -\text {ArcTan}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1 \\ y(x)\to \text {ArcTan}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1 \\ \end{align*}