Internal problem ID [8007]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 427.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (3 x +5\right ) \left (y^{\prime }\right )^{2}-\left (3 y+x \right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.217 (sec). Leaf size: 50
dsolve((3*x+5)*diff(y(x),x)^2-(3*y(x)+x)*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-3 c_{1}^{2}+c_{1}\right ) x}{-3 c_{1}+1}-\frac {5 c_{1}^{2}}{-3 c_{1}+1} \\ y \relax (x ) = \frac {x}{3}+\frac {10}{9}+\sqrt {5+3 x}\, c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 80
DSolve[y[x] - (x + 3*y[x])*y'[x] + (5 + 3*x)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+\frac {5 c_1}{-1+3 c_1}\right ) \\ y(x)\to \frac {1}{9} \left (3 x-2 \sqrt {5} \sqrt {3 x+5}+10\right ) \\ y(x)\to \frac {1}{9} \left (3 x+2 \sqrt {5} \sqrt {3 x+5}+10\right ) \\ \end{align*}