60.1.416 problem 427

Internal problem ID [10430]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 427
Date solved : Sunday, March 30, 2025 at 04:41:46 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

\begin{align*} \left (3 x +5\right ) {y^{\prime }}^{2}-\left (3 y+x \right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.076 (sec). Leaf size: 60

ode:=(3*x+5)*diff(y(x),x)^2-(3*y(x)+x)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {x}{3}+\frac {10}{9}-\frac {2 \sqrt {15 x +25}}{9} \\ y &= \frac {x}{3}+\frac {10}{9}+\frac {2 \sqrt {15 x +25}}{9} \\ y &= \frac {\left (3 x +5\right ) c_1^{2}-c_1 x}{3 c_1 -1} \\ \end{align*}

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 80

ode=y[x] - (x + 3*y[x])*D[y[x],x] + (5 + 3*x)*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x - 3*y(x))*Derivative(y(x), x) + (3*x + 5)*Derivative(y(x), x)**2 + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out