76.17.21 problem 30

Internal problem ID [17707]
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 4.7 (Variation of parameters). Problems at page 280
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 11:01:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 18

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

\[ y = t \left (4 t \ln \left (t \right )+\left (c_{2} -4\right ) t +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 21

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

\[ y(t)\to t (4 t \log (t)+(-4+c_2) t+c_1) \]