75.5.7 problem 106

Internal problem ID [16672]
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 : 106
Date solved : Monday, March 31, 2025 at 03:04:45 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 4 x -3 y+\left (2 y-3 x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 51

ode:=4*x-3*y(x)+(2*y(x)-3*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {3 c_1 x -\sqrt {x^{2} c_1^{2}+4}}{2 c_1} \\ y &= \frac {3 c_1 x +\sqrt {x^{2} c_1^{2}+4}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.414 (sec). Leaf size: 95

ode=(4*x-3*y[x])+(2*y[x]-3*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.200 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x + (-3*x + 2*y(x))*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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