85.71.1 problem 3

Internal problem ID [22933]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 6. Solution of linear differential equations by Laplace transform. C Exercises at page 284
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:16:44 PM
CAS classification : [_Laguerre, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t y^{\prime \prime }-t y^{\prime }+y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.049 (sec). Leaf size: 5

ode:=t*diff(diff(y(t),t),t)-t*diff(y(t),t)+y(t) = 0; 
ic:=[y(0) = 0, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = t \]

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to t \end{align*}

✗ Sympy

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

ValueError : Couldnt solve for initial conditions