73.6.16 problem 7.5 (f)

Internal problem ID [15076]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.5 (f)
Date solved : Thursday, March 13, 2025 at 05:36:28 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = {\mathrm e}^{x^{2}} c_{1} -1 \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 20

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

\begin{align*} y(x)\to -1+c_1 e^{x^2} \\ y(x)\to -1 \\ \end{align*}

✓ Sympy. Time used: 0.261 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} e^{x^{2}} - 1 \]