77.1.12 problem 26 (page 31)

Internal problem ID [17831]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 26 (page 31)
Date solved : Monday, March 31, 2025 at 04:35:03 PM
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 } \end{align*}

✓ Maple. Time used: 0.265 (sec). Leaf size: 717

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

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

✓ Mathematica. Time used: 60.665 (sec). Leaf size: 7785

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

Too large to display

✓ Sympy. Time used: 1.104 (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)
 

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