Internal problem ID [14869]
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: 48.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-8 y^{\prime }+16 y=\frac {{\mathrm e}^{4 t}}{t^{3}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(t),t$2)-8*diff(y(t),t)+16*y(t)=1/t^3*exp(4*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{4 t} \left (2 c_{1} t^{2}+2 t c_{2} +1\right )}{2 t} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 31
DSolve[y''[t]-8*y'[t]+16*y[t]==1/t^3*Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{4 t} \left (2 c_2 t^2+2 c_1 t+1\right )}{2 t} \]