Internal problem ID [161]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 15
dsolve([diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 15
DSolve[{y''[x]-3*y'[x]+2*y[x]==0,{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^x \left (e^x-2\right ) \\ \end{align*}