Internal problem ID [8763]
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]
\[ \boxed {\left (3 x +5\right ) {y^{\prime }}^{2}-\left (x +3 y\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 60
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 \left (x \right ) &= \frac {x}{3}+\frac {10}{9}-\frac {2 \sqrt {15 x +25}}{9} \\ y \left (x \right ) &= \frac {x}{3}+\frac {10}{9}+\frac {2 \sqrt {15 x +25}}{9} \\ y \left (x \right ) &= \frac {\left (3 x +5\right ) c_{1}^{2}-c_{1} x}{3 c_{1} -1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.021 (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*}