89.3.19 problem 19

Internal problem ID [24317]
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. Exercises at page 34
Problem number : 19
Date solved : Thursday, October 02, 2025 at 10:17:45 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 22

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

\[ y = \frac {-x +c_1}{\sin \left (x^{2}\right )-x^{2}} \]

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 1.373 (sec). Leaf size: 14

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

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