86.4.1 problem 1

Internal problem ID [23108]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 4. Linear equations of the first order. Exercise 4b at page 64
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:22:03 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-2 y \cos \left (x \right )&={\mathrm e}^{x} \sin \left (x \right )^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=x*diff(y(x),x)-2*y(x)*cos(x) = exp(x)*sin(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\int \frac {\sin \left (x \right )^{3} {\mathrm e}^{x -2 \,\operatorname {Ci}\left (x \right )}}{x}d x +c_1 \right ) {\mathrm e}^{2 \,\operatorname {Ci}\left (x \right )} \]

✓ Mathematica. Time used: 0.757 (sec). Leaf size: 42

ode=x*D[y[x],x]-2*y[x]*Cos[x]==Exp[x]*Sin[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 \operatorname {CosIntegral}(x)} \left (\int _1^x\frac {e^{K[1]-2 \operatorname {CosIntegral}(K[1])} \sin ^3(K[1])}{K[1]}dK[1]+c_1\right ) \end{align*}

✗ Sympy

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

Timed Out