Internal problem ID [14596]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=\frac {{\mathrm e}^{2 t}}{t^{2}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=1/t^2*exp(2*t),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{2 t} \left (-1+c_{1} t -\ln \left (t \right )+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 23
DSolve[y''[t]-4*y'[t]+4*y[t]==1/t^2*Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{2 t} (-\log (t)+c_2 t-1+c_1) \]