Internal problem ID [621]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+3 y^{\prime }-2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -\beta ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve([2*diff(y(x),x$2) +3*diff(y(x),x)-2*y(x) = 0,y(0) = 1, D(y)(0) = -beta],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (2 \,{\mathrm e}^{\frac {5 x}{2}} \beta -4 \,{\mathrm e}^{\frac {5 x}{2}}-2 \beta -1\right ) {\mathrm e}^{-2 x}}{5} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 67
DSolve[{y''[x]+3*y'[x]-2*y[x]==0,{y[0]==1,y'[0]==-\[Beta]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{34} e^{-\frac {1}{2} \left (3+\sqrt {17}\right ) x} \left (2 \sqrt {17} \beta +\left (-2 \sqrt {17} \beta +3 \sqrt {17}+17\right ) e^{\sqrt {17} x}-3 \sqrt {17}+17\right ) \\ \end{align*}