76.12.17 problem 29

Internal problem ID [17573]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 10:44:23 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

dsolve([t^2*diff(y(t),t$2)-4*t*diff(y(t),t)+6*y(t)=0,t^2],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 16

DSolve[t^2*D[y[t],{t,2}]-4*t*D[y[t],t]+6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^2 (c_2 t+c_1) \]