Internal problem ID [13293]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 17. Second order Homogeneous equations with constant coefficients. Additional
exercises page 334
Problem number: 17.6 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+13 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(y(x),x$2)-4*diff(y(x),x)+13*y(x)=0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y = \frac {{\mathrm e}^{2 x} \sin \left (3 x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 18
DSolve[{y''[x]-4*y'[x]+13*y[x]==0,{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{2 x} \sin (3 x) \]