10.7.20 problem 22

Internal problem ID [1268]
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 : 22
Date solved : Monday, January 27, 2025 at 04:48:29 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=\beta \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 22

dsolve([4*diff(y(x),x$2) -y(x) = 0,y(0) = 2, D(y)(0) = beta],y(x), singsol=all)
 

\[ y = \left (\beta +1\right ) {\mathrm e}^{\frac {x}{2}}-\left (-1+\beta \right ) {\mathrm e}^{-\frac {x}{2}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 25

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

\[ y(x)\to e^{-x/2} \left (-\beta +(\beta +1) e^x+1\right ) \]