87.10.14 problem 15

Internal problem ID [23415]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 79
Problem number : 15
Date solved : Friday, October 03, 2025 at 08:03:44 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.371 (sec). Leaf size: 309

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve y(x) - sin(x) + cos(x)*Derivative(y(x), (x, 2))