89.6.45 problem 46

Internal problem ID [24428]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 46
Date solved : Thursday, October 02, 2025 at 10:29:16 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

\[ y = \sqrt {x -1}\, \sqrt {x +1}\, c_1 -x^{3}+x \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.291 (sec). Leaf size: 17

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

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