75.5.10 problem 109

Internal problem ID [16667]
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 : 109
Date solved : Thursday, March 13, 2025 at 08:30:34 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 2.605 (sec). Leaf size: 1814

ode:=3*y(x)-7*x+7-(3*x-7*y(x)-3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 60.671 (sec). Leaf size: 7785

ode=(3*y[x]-7*x+7)-(3*x-7*y[x]-3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✓ Sympy. Time used: 1.048 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-7*x - (3*x - 7*y(x) - 3)*Derivative(y(x), x) + 3*y(x) + 7,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (y{\left (x \right )} \right )} = C_{1} - \log {\left (\left (\frac {x - 1}{y{\left (x \right )}} - 1\right )^{\frac {2}{7}} \left (\frac {x - 1}{y{\left (x \right )}} + 1\right )^{\frac {5}{7}} \right )} \]