74.12.27 problem 27

Internal problem ID [16334]
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 : 27
Date solved : Tuesday, January 28, 2025 at 09:05:00 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} \sqrt {-t^{2}+1} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 36

dsolve(diff(y(t),t$2)-2*diff(y(t),t)+y(t)=exp(t)*sqrt(1-t^2),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{t} \left (\left (t^{2}+2\right ) \sqrt {-t^{2}+1}+6 c_{1} t +3 \arcsin \left (t \right ) t +6 c_{2} \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 55

DSolve[D[y[t],{t,2}]-2*D[y[t],t]+y[t]==Exp[t]*Sqrt[1-t^2],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{6} e^t \left (3 t \arcsin (t)+\sqrt {1-t^2} t^2+2 \sqrt {1-t^2}+6 c_2 t+6 c_1\right ) \]