32.2.7 problem Differential equations with Linear Coefficients. Exercise 8.7, page 69

Internal problem ID [5791]
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 8.7, page 69
Date solved : Tuesday, March 04, 2025 at 11:45:17 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y \left (x \right ) = \frac {3}{7}+\frac {c_{1}}{\left (2 x +1\right )^{{7}/{2}}} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 28

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

\begin{align*} y(x)\to \frac {3}{7}+\frac {c_1}{(2 x+1)^{7/2}} \\ y(x)\to \frac {3}{7} \\ \end{align*}

✓ Sympy. Time used: 0.366 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = \frac {C_{1}}{\sqrt {2 x + 1} \left (8 x^{3} + 12 x^{2} + 6 x + 1\right )} + \frac {3}{7} \]