Internal problem ID [1089]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page
203
Problem number: 2d.
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 }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = k_{0}, y^{\prime }\relax (0) = k_{1}] \end {align*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=0,y(0) = k__0, D(y)(0) = k__1],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} \left (\left (k_{1}-k_{0}\right ) \sin \relax (x )+k_{0} \cos \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[{y''[x]-2*y'[x]+2*y[x]==0,{y[0]==k0,y'[0]==k1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x ((\text {k1}-\text {k0}) \sin (x)+\text {k0} \cos (x)) \\ \end{align*}