64.10.38 problem 38

Internal problem ID [13444]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 38
Date solved : Tuesday, January 28, 2025 at 05:42:47 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+37 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 22

dsolve([4*diff(y(x),x$2)+4*diff(y(x),x)+37*y(x)=0,y(0) = 2, D(y)(0) = -4],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x}{2}} \left (-\sin \left (3 x \right )+2 \cos \left (3 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 26

DSolve[{4*D[y[x],{x,2}]+4*D[y[x],x]+37*y[x]==0,{y[0]==2,Derivative[1][y][0] ==-4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/2} (2 \cos (3 x)-\sin (3 x)) \]