40.2.2 problem 25

Internal problem ID [6580]
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 : 25
Date solved : Sunday, March 30, 2025 at 11:10:20 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = -\frac {1}{2}+\frac {\sqrt {x -2}\, c_1}{\sqrt {x +2}} \]

✓ Mathematica. Time used: 0.087 (sec). Leaf size: 87

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

\begin{align*} y(x)\to \frac {\sqrt {2-x} \left (\sqrt {4-x^2}-2 \sqrt {x+2}+2 c_1 \left (x+2 \sqrt {2-x}-2\right )\right )}{2 \sqrt {x+2} \left (x+2 \sqrt {2-x}-2\right )} \\ y(x)\to -\frac {1}{2} \\ \end{align*}

✓ Sympy. Time used: 0.320 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {C_{1} \sqrt {x - 2}}{\sqrt {x + 2}} - \frac {1}{2} \]