Internal problem ID [4256]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1031.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+y b=0} \]
✓ Solution by Maple
Time used: 0.218 (sec). Leaf size: 67
dsolve(diff(y(x),x)^3-(b*x+a)*diff(y(x),x)+b*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {2 \sqrt {3 x b +3 a}\, \left (x b +a \right )}{9 b} y \left (x \right ) = \frac {2 \sqrt {3 x b +3 a}\, \left (x b +a \right )}{9 b} y \left (x \right ) = c_{1} x +\frac {-c_{1}^{3}+a c_{1}}{b} \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 72
DSolve[(y'[x])^3 -(a+b x)y'[x]+b y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 \left (a+b x-c_1{}^2\right )}{b} y(x)\to -\frac {2 (a+b x)^{3/2}}{3 \sqrt {3} b} y(x)\to \frac {2 (a+b x)^{3/2}}{3 \sqrt {3} b} \end{align*}