Internal problem ID [3778]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1066.
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: 0.105 (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: 0.011 (sec). Leaf size: 64
DSolve[(a^2-x^2) (y'[x])^3 +b x (a^2-x^2) (y'[x])^2 -y'[x] -b x==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*}