40.2.14 problem 39

Internal problem ID [6592]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 39
Date solved : Wednesday, March 05, 2025 at 01:01:10 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.200 (sec). Leaf size: 1814

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

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

✓ Mathematica. Time used: 60.747 (sec). Leaf size: 7785

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

Too large to display

✓ Sympy. Time used: 1.111 (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)
 

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