32.7.33 problem Exercise 20, problem 34, page 220

Internal problem ID [5948]
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 34, page 220
Date solved : Monday, January 27, 2025 at 01:28:05 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.048 (sec). Leaf size: 25

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+20*y(x)=0,y(1/2*Pi) = 1, D(y)(1/2*Pi) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 31

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+20*y[x]==0,{y[Pi/2]==1,Derivative[1][y][Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

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