76.13.40 problem 40

Internal problem ID [17622]
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 : 40
Date solved : Tuesday, January 28, 2025 at 10:45:48 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+y^{\prime }-4 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.071 (sec). Leaf size: 30

dsolve([2*diff(y(x),x$2)+diff(y(x),x)-4*y(x)=0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = \frac {2 \left ({\mathrm e}^{\frac {\left (-1+\sqrt {33}\right ) x}{4}}-{\mathrm e}^{-\frac {\left (1+\sqrt {33}\right ) x}{4}}\right ) \sqrt {33}}{33} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 40

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

\[ y(x)\to \frac {2 e^{-\frac {1}{4} \left (1+\sqrt {33}\right ) x} \left (e^{\frac {\sqrt {33} x}{2}}-1\right )}{\sqrt {33}} \]