10.10.19 problem 29

Internal problem ID [1351]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page 190
Problem number : 29
Date solved : Monday, January 27, 2025 at 04:52:02 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = t \left (4 t \ln \left (t \right )+\left (c_1 -4\right ) t +c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (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]
 

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