74.18.4 problem 10

Internal problem ID [16561]
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 : Tuesday, January 28, 2025 at 09:10:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

Using reduction of order method given that one solution is

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

✓ Solution by Maple

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

dsolve([(t+1)^2*diff(y(t),t$2)-2*(t+1)*diff(y(t),t)+2*y(t)=0,t+1],singsol=all)
 

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

✓ Solution by Mathematica

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

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

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