76.13.38 problem 38

Internal problem ID [17620]
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 : 38
Date solved : Tuesday, January 28, 2025 at 10:45:43 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 38

dsolve([diff(y(x),x$2)+6*diff(y(x),x)+3*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\left (2-\sqrt {6}\right ) {\mathrm e}^{-\left (3+\sqrt {6}\right ) x}}{4}+\frac {{\mathrm e}^{\left (-3+\sqrt {6}\right ) x} \left (2+\sqrt {6}\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 48

DSolve[{D[y[x],{x,2}]+6*D[y[x],x]+3*y[x]==0,{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-\left (\left (3+\sqrt {6}\right ) x\right )} \left (\left (2+\sqrt {6}\right ) e^{2 \sqrt {6} x}+2-\sqrt {6}\right ) \]