88.9.8 problem 8

Internal problem ID [24028]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 48
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:54:37 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {y}{-x^{2}+1}&=3 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 34

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

\[ y = \frac {\left (3 \sqrt {-x^{2}+1}+3 \arcsin \left (x \right )+c_1 \right ) \left (x +1\right )}{\sqrt {-x^{2}+1}} \]

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 58

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

\begin{align*} y(x)&\to \frac {\sqrt {x+1} \left (-6 \arctan \left (\frac {\sqrt {1-x^2}}{x-1}\right )+3 \sqrt {1-x^2}+c_1\right )}{\sqrt {1-x}} \end{align*}

✓ Sympy. Time used: 7.386 (sec). Leaf size: 231

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

\[ y{\left (x \right )} = \begin {cases} \frac {C_{1} \sqrt {x + 1}}{- i \sqrt {1 - x} + \sqrt {x - 1} + \sqrt {x + 1} \left (\begin {cases} \frac {\sqrt {x - 1}}{\sqrt {x + 1}} & \text {for}\: \left |{x + 1}\right | > 2 \\\frac {i \sqrt {1 - x}}{\sqrt {x + 1}} & \text {otherwise} \end {cases}\right )} - \frac {3 i \sqrt {1 - x}}{- i \sqrt {1 - x} + \sqrt {x - 1} + \sqrt {x + 1} \left (\begin {cases} \frac {\sqrt {x - 1}}{\sqrt {x + 1}} & \text {for}\: \left |{x + 1}\right | > 2 \\\frac {i \sqrt {1 - x}}{\sqrt {x + 1}} & \text {otherwise} \end {cases}\right )} + \frac {3 \sqrt {x + 1} \int \frac {x^{2}}{x \sqrt {x - 1} \sqrt {x + 1} + \sqrt {x - 1} \sqrt {x + 1}}\, dx}{- i \sqrt {1 - x} + \sqrt {x - 1} + \sqrt {x + 1} \left (\begin {cases} \frac {\sqrt {x - 1}}{\sqrt {x + 1}} & \text {for}\: \left |{x + 1}\right | > 2 \\\frac {i \sqrt {1 - x}}{\sqrt {x + 1}} & \text {otherwise} \end {cases}\right )} & \text {for}\: x \geq -3 \wedge x \leq 1 \\\text {NaN} & \text {otherwise} \end {cases} \]