10.7.11 problem 11

Internal problem ID [1259]
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
Date solved : Monday, January 27, 2025 at 04:48:08 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime }-5 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (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)
 

\[ y = -8 \,{\mathrm e}^{\frac {x}{2}}+12 \,{\mathrm e}^{\frac {x}{3}} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 48

DSolve[{6*D[y[x],{x,2}]-5*D[y[x],x]+2*y[x]==0,{y[0]==4,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4}{23} e^{5 x/12} \left (23 \cos \left (\frac {\sqrt {23} x}{12}\right )-5 \sqrt {23} \sin \left (\frac {\sqrt {23} x}{12}\right )\right ) \]