Internal problem ID [8857]
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]
\[ \boxed {{y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 44
dsolve(diff(y(x),x)^3-(x+5)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {2 \sqrt {3 x +15}\, \left (x +5\right )}{9} \\ y \left (x \right ) &= \frac {2 \sqrt {3 x +15}\, \left (x +5\right )}{9} \\ y \left (x \right ) &= c_{1} \left (-c_{1}^{2}+x +5\right ) \\ \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*}