32.2.10 problem Differential equations with Linear Coefficients. Exercise 8.10, page 69

Internal problem ID [5794]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number : Differential equations with Linear Coefficients. Exercise 8.10, page 69
Date solved : Sunday, March 30, 2025 at 10:16:49 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.197 (sec). Leaf size: 33

ode:=3*x-2*y(x)+4-(2*x+7*y(x)-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {7+15625 \left (x +\frac {26}{25}\right )^{2} c_1^{2}}+\left (-50 x +25\right ) c_1}{175 c_1} \]

✓ Mathematica. Time used: 0.14 (sec). Leaf size: 65

ode=(3*x-2*y[x]+4)-(2*x+7*y[x]-1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{7} \left (-\sqrt {25 x^2+52 x+1+49 c_1}-2 x+1\right ) \\ y(x)\to \frac {1}{7} \left (\sqrt {25 x^2+52 x+1+49 c_1}-2 x+1\right ) \\ \end{align*}

✓ Sympy. Time used: 2.369 (sec). Leaf size: 51

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x - (2*x + 7*y(x) - 1)*Derivative(y(x), x) - 2*y(x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {2 x}{7} - \frac {\sqrt {C_{1} + 625 x^{2} + 1300 x}}{35} + \frac {1}{7}, \ y{\left (x \right )} = - \frac {2 x}{7} + \frac {\sqrt {C_{1} + 625 x^{2} + 1300 x}}{35} + \frac {1}{7}\right ] \]