Internal problem ID [14601]
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: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y={\mathrm e}^{-2 t} \sqrt {-t^{2}+1}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(t),t$2)+4*diff(y(t),t)+4*y(t)=exp(-2*t)*sqrt(1-t^2),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\left (t^{2}+2\right ) \sqrt {-t^{2}+1}+6 c_{1} t +3 \arcsin \left (t \right ) t +6 c_{2} \right ) {\mathrm e}^{-2 t}}{6} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 73
DSolve[y''[t]+4*y'[t]+4*y[t]==Exp[-2*t]*Sqrt[1-t^2],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{6} e^{-2 t} \left (-6 t \arctan \left (\frac {\sqrt {1-t^2}}{t+1}\right )+\sqrt {1-t^2} t^2+2 \sqrt {1-t^2}+6 c_2 t+6 c_1\right ) \]