Internal problem ID [14604]
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: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y={\mathrm e}^{2 t} \arctan \left (t \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 38
dsolve(diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=exp(2*t)*arctan(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{2 t} \left (\arctan \left (t \right ) t^{2}-\ln \left (t^{2}+1\right ) t +2 c_{1} t -\arctan \left (t \right )+2 c_{2} +t \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 42
DSolve[y''[t]-4*y'[t]+4*y[t]==Exp[2*t]*ArcTan[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{2 t} \left (\left (t^2-1\right ) \arctan (t)-t \log \left (t^2+1\right )+t+2 c_2 t+2 c_1\right ) \]