Internal problem ID [612]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant
Coefficients, page 144
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+y^{\prime }-4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.052 (sec). Leaf size: 30
dsolve([2*diff(y(x),x$2) +diff(y(x),x)-4*y(x) = 0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 \left (-{\mathrm e}^{\frac {\left (-1+\sqrt {33}\right ) x}{4}}+{\mathrm e}^{-\frac {\left (1+\sqrt {33}\right ) x}{4}}\right ) \sqrt {33}}{33} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 30
DSolve[{2*y''[x]+y'[x]-4*y[x]==0,{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 e^{-x/4} \sinh \left (\frac {\sqrt {33} x}{4}\right )}{\sqrt {33}} \\ \end{align*}