Internal problem ID [8102]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 522.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-\left (x +5\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.251 (sec). Leaf size: 26
dsolve(diff(y(x),x)^3-(x+5)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -c_{1}^{3}+c_{1} x +5 c_{1} \\ y \relax (x ) = c_{1} \left (x +5\right )^{\frac {3}{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 57
DSolve[y[x] - (5 + x)*y'[x] + y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+5-c_1{}^2\right ) \\ y(x)\to -\frac {2 (x+5)^{3/2}}{3 \sqrt {3}} \\ y(x)\to \frac {2 (x+5)^{3/2}}{3 \sqrt {3}} \\ \end{align*}