49.8.1 problem 1(c)

Internal problem ID [7648]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 79
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:08:58 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 17

dsolve([diff(y(x),x$3)-4*diff(y(x),x)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{2 x}}{4}-\frac {{\mathrm e}^{-2 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 69

DSolve[{D[y[x],{x,3}]-4*y[x]==0,{y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-\frac {x}{\sqrt [3]{2}}} \left (e^{\frac {3 x}{\sqrt [3]{2}}}+\sqrt {3} \sin \left (\frac {\sqrt {3} x}{\sqrt [3]{2}}\right )-\cos \left (\frac {\sqrt {3} x}{\sqrt [3]{2}}\right )\right )}{3\ 2^{2/3}} \]