90.20.35 problem 22

Internal problem ID [25330]
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 : 22
Date solved : Friday, October 03, 2025 at 08:08:56 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+t^{2} y&=\cos \left (t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=y_{1} \\ y^{\prime }\left (0\right )&=y_{1} \\ \end{align*}

✓ Maple. Time used: 0.217 (sec). Leaf size: 277

ode:=(t^2+1)*diff(diff(y(t),t),t)-t*diff(y(t),t)+t^2*y(t) = cos(t); 
ic:=[y(0) = y__1, D(y)(0) = y__1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✗ Mathematica

ode=(1+t^2)*D[y[t],{t,2}]-t*D[y[t],t]+t^2*y[t]==Cos[t]; 
ic={y[0]==y1,Derivative[1][y][0] ==y1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y1 = symbols("y1") 
y = Function("y") 
ode = Eq(t**2*y(t) - t*Derivative(y(t), t) + (t**2 + 1)*Derivative(y(t), (t, 2)) - cos(t),0) 
ics = {y(0): y1, Subs(Derivative(y(t), t), t, 0): y1} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(t), t) - (t**2*(y(t) + Derivative(y(t), (t, 2))) -