67.2.37 problem Problem 18(b)

Internal problem ID [13923]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 18(b)
Date solved : Monday, March 31, 2025 at 08:18:13 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = \left (c_1 \int \frac {{\mathrm e}^{\operatorname {Si}\left (x \right )}}{x^{2}}d x +c_2 \right ) {\mathrm e}^{-\operatorname {Si}\left (x \right )} x \]

✗ Mathematica

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

Not solved

✗ Sympy

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

False