Internal problem ID [8006]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 426.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {\left (3 x +1\right ) \left (y^{\prime }\right )^{2}-3 \left (y+2\right ) y^{\prime }+9=0} \end {gather*}
✓ Solution by Maple
Time used: 0.248 (sec). Leaf size: 35
dsolve((3*x+1)*diff(y(x),x)^2-3*(y(x)+2)*diff(y(x),x)+9 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x +\frac {c_{1}^{2}-6 c_{1}+9}{3 c_{1}} \\ y \relax (x ) = \sqrt {1+3 x}\, c_{1}-2 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 60
DSolve[9 - 3*(2 + y[x])*y'[x] + (1 + 3*x)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+\frac {1}{3}\right )-2+\frac {3}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \left (\sqrt {3 x+1}+1\right ) \\ y(x)\to 2 \left (\sqrt {3 x+1}-1\right ) \\ \end{align*}