Internal problem ID [167]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 11.
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) = 0, y^{\prime }\relax (0) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 10
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=0,y(0) = 0, D(y)(0) = 5],y(x), singsol=all)
\[ y \relax (x ) = 5 \sin \relax (x ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 12
DSolve[{y''[x]-2*y'[x]+2*y[x]==0,{y[0]==0,y'[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 5 e^x \sin (x) \\ \end{align*}