75.5.13 problem 112

Internal problem ID [16678]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 112
Date solved : Monday, March 31, 2025 at 03:05:08 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.131 (sec). Leaf size: 33

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

\[ y = \frac {-\sqrt {5 \left (x -1\right )^{2} c_1^{2}+4}+\left (-3 x +5\right ) c_1}{2 c_1} \]

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 65

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

\begin{align*} y(x)\to \frac {1}{2} \left (-\sqrt {5 x^2-10 x+25+4 c_1}-3 x+5\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5 x^2-10 x+25+4 c_1}-3 x+5\right ) \\ \end{align*}

✓ Sympy. Time used: 2.187 (sec). Leaf size: 51

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

\[ \left [ y{\left (x \right )} = - \frac {3 x}{2} - \frac {\sqrt {C_{1} + 5 x^{2} - 10 x}}{2} + \frac {5}{2}, \ y{\left (x \right )} = - \frac {3 x}{2} + \frac {\sqrt {C_{1} + 5 x^{2} - 10 x}}{2} + \frac {5}{2}\right ] \]