Internal problem ID [1090]
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: 3c.
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 }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 7, y^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(0) = 7, D(y)(0) = 4],y(x), singsol=all)
\[ y \relax (x ) = \left (-3 x +7\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 14
DSolve[{y''[x]-2*y'[x]+y[x]==0,{y[0]==7,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (7-3 x) \\ \end{align*}