Internal problem ID [206]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.3, second order linear equations. Page 323
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+25 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)-6*diff(y(x),x)+25*y(x)=0,y(0) = 4, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{3 x} \left (-11 \sin \left (4 x \right )+16 \cos \left (4 x \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 27
DSolve[{y''[x]-6*y'[x]+25*y[x]==0,{y[0]==4,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{3 x} (16 \cos (4 x)-11 \sin (4 x)) \\ \end{align*}