76.13.18 problem 18

Internal problem ID [17600]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 10:45:01 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+125/100*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} \left (c_{1} \sin \left (\frac {x}{2}\right )+c_{2} \cos \left (\frac {x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+125/100*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (c_2 \cos \left (\frac {x}{2}\right )+c_1 \sin \left (\frac {x}{2}\right )\right ) \]