Internal problem ID [1087]
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: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-7 y^{\prime }+10 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(x),x$2)-7*diff(y(x),x)+10*y(x)=0,y(0) = -1, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -2 \,{\mathrm e}^{2 x}+{\mathrm e}^{5 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[{y''[x]-7*y'[x]+10*y[x]==0,{y[0]==-1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} \left (e^{3 x}-2\right ) \\ \end{align*}