76.13.39 problem 39

Internal problem ID [17621]
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 : 39
Date solved : Tuesday, January 28, 2025 at 10:45:45 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)+diff(y(x),x)+125/100*y(x)=0,y(0) = 3, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {x}{2}} \left (5 \sin \left (x \right )+6 \cos \left (x \right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 25

DSolve[{D[y[x],{x,2}]+D[y[x],x]+125/100*y[x]==0,{y[0]==3,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-x/2} (5 \sin (x)+6 \cos (x)) \]