32.7.32 problem Exercise 20, problem 33, page 220

Internal problem ID [5947]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20, problem 33, page 220
Date solved : Monday, January 27, 2025 at 01:28:02 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)-2*diff(y(x),x)+5*y(x)=0,y(0) = 2, D(y)(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{2} e^x (4 \cos (2 x)-\sin (2 x)) \]