7.10.23 problem 23

Internal problem ID [293]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 23
Date solved : Wednesday, February 05, 2025 at 03:06:48 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=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: 0.013 (sec). Leaf size: 22

dsolve([diff(y(x),x$2)-6*diff(y(x),x)+25*y(x)=0,y(0) = 3, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} \left (-2 \sin \left (4 x \right )+3 \cos \left (4 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 24

DSolve[{D[y[x],{x,2}]-6*D[y[x],x]+25*y[x]==0,{y[0]==3,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} (3 \cos (4 x)-2 \sin (4 x)) \]