Internal problem ID [4095]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.009 (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)
\[ y \relax (x ) = -\frac {{\mathrm e}^{x} \left (\sin \left (2 x \right )-4 \cos \left (2 x \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 25
DSolve[{y''[x]-2*y'[x]+5*y[x]==0,{y[0]==2,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^x (4 \cos (2 x)-\sin (2 x)) \\ \end{align*}