11.21 problem 17.4 (c)

Internal problem ID [13599]

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: 17.4 (c).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

\[ \boxed {y^{\prime \prime }-8 y^{\prime }+16 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 14] \end {align*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)-8*diff(y(x),x)+16*y(x)=0,y(0) = 3, D(y)(0) = 14],y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{4 x} \left (3+2 x \right ) \]

Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 16

DSolve[{y''[x]-8*y'[x]+16*y[x]==0,{y[0]==3,y'[0]==14}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{4 x} (2 x+3) \]