Internal problem ID [4604]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+20 y=0} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 1, y^{\prime }\left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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: 0.019 (sec). Leaf size: 31
DSolve[{y''[x]-4*y'[x]+20*y[x]==0,{y[Pi/2]==1,y'[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{2 x-\pi } (4 \cos (4 x)-\sin (4 x)) \]