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: 0.047 (sec). Leaf size: 65
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 b x +3 a}\, \left (b x +a \right )}{9 b} \\ y \left (x \right ) &= \frac {2 \sqrt {3 b x +3 a}\, \left (b x +a \right )}{9 b} \\ y \left (x \right ) &= \frac {c_{1} \left (b x -c_{1}^{2}+a \right )}{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*}