76.13.32 problem 32

Internal problem ID [17614]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 10:45:29 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: 0.019 (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: 0.013 (sec). Leaf size: 24

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

\[ y(x)\to 12 e^{x/3}-8 e^{x/2} \]