78.3.17 problem 5 (e)

Internal problem ID [18049]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 5 (e)
Date solved : Monday, March 31, 2025 at 05:00:02 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \left (x +1\right )^{{3}/{4}} c_1 +2 x +3 \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 20

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

\[ y(x)\to 2 x+c_1 (x+1)^{3/4}+3 \]

✓ Sympy. Time used: 1.406 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} \left (x + 1\right )^{\frac {3}{4}} + 2 x + 3 \]