74.18.4 problem 10

Internal problem ID [16482]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 10
Date solved : Thursday, March 13, 2025 at 08:14:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (t +1\right )^{2} y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+2 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=t +1 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 15

ode:=(t+1)^2*diff(diff(y(t),t),t)-2*(t+1)*diff(y(t),t)+2*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (t +1\right ) \left (c_{1} \left (t +1\right )+c_{2} \right ) \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 18

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

\[ y(t)\to (t+1) (c_2 (t+1)+c_1) \]

✓ Sympy. Time used: 0.249 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = C_{1} \left (t + 1\right )^{\frac {3}{2}} \]