76.13.34 problem 34

Internal problem ID [17616]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 34
Date solved : Tuesday, January 28, 2025 at 10:45:32 AM
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 (\frac {\pi }{2}\right )&=0\\ y^{\prime }\left (\frac {\pi }{2}\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

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

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