Internal problem ID [616]
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: 20.
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 }+y=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = 2, y^{\prime }\relax (0) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 15
dsolve([2*diff(y(x),x$2) -3*diff(y(x),x)+y(x) = 0,y(0) = 2, D(y)(0) = 1/2],y(x), singsol=all)
\[ y \relax (x ) = 3 \,{\mathrm e}^{\frac {x}{2}}-{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[{2*y''[x]-3*y'[x]+y[x]==0,{y[0]==2,y'[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 e^{x/2}-e^x \\ \end{align*}