90.20.34 problem 21

Internal problem ID [25329]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 337
Problem number : 21
Date solved : Friday, October 03, 2025 at 12:00:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=y_{1} \\ y^{\prime }\left (\frac {\pi }{2}\right )&=y_{1} \\ \end{align*}

✗ Maple

ode:=sin(t)*diff(diff(y(t),t),t)+y(t) = cos(t); 
ic:=[y(1/2*Pi) = y__1, D(y)(1/2*Pi) = y__1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=Sin[t]*D[y[t],{t,2}]+y[t]==Cos[t]; 
ic={y[Pi/2]==y1,Derivative[1][y][Pi/2] ==y1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
t = symbols("t") 
y1 = symbols("y1") 
y = Function("y") 
ode = Eq(y(t) + sin(t)*Derivative(y(t), (t, 2)) - cos(t),0) 
ics = {y(pi/2): y1, Subs(Derivative(y(t), t), t, pi/2): y1} 
dsolve(ode,func=y(t),ics=ics)
 

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