Internal problem ID [609]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {6 y^{\prime \prime }-5 y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([6*diff(y(x),x$2) -5*diff(y(x),x)+y(x) = 0,y(0) = 4, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -8 \,{\mathrm e}^{\frac {x}{2}}+12 \,{\mathrm e}^{\frac {x}{3}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 48
DSolve[{6*y''[x]-5*y'[x]+2*y[x]==0,{y[0]==4,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4}{23} e^{5 x/12} \left (23 \cos \left (\frac {\sqrt {23} x}{12}\right )-5 \sqrt {23} \sin \left (\frac {\sqrt {23} x}{12}\right )\right ) \\ \end{align*}