67.4.10 problem 5.1 (j)

Internal problem ID [16379]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.1 (j)
Date solved : Thursday, October 02, 2025 at 01:26:55 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+\cos \left (x^{2}\right )&=827 y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=x*diff(y(x),x)+cos(x^2) = 827*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-\int \frac {\cos \left (x^{2}\right )}{x^{828}}d x +c_1 \right ) x^{827} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 30

ode=x*D[y[x],x]+Cos[x^2]==827*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^{827} \left (\int _1^x-\frac {\cos \left (K[1]^2\right )}{K[1]^{828}}dK[1]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - 827*y(x) + cos(x**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out