64.10.33 problem 33

Internal problem ID [13439]
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 : 33
Date solved : Tuesday, January 28, 2025 at 05:42:33 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+29 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 13

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+29*y(x)=0,y(0) = 0, D(y)(0) = 5],y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \sin \left (5 x \right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 15

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+29*y[x]==0,{y[0]==0,Derivative[1][y][0] ==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \sin (5 x) \]