32.7.34 problem Exercise 20, problem 35, page 220

Internal problem ID [5949]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20, problem 35, page 220
Date solved : Monday, January 27, 2025 at 01:28:09 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=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 )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 21

dsolve([3*diff(y(x),x$3)+5*diff(y(x),x$2)+diff(y(x),x)-y(x)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = -1],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (9 \,{\mathrm e}^{\frac {4 x}{3}}+4 x -9\right ) {\mathrm e}^{-x}}{16} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 28

DSolve[{3*D[y[x],{x,3}]+5*D[y[x],{x,2}]+D[y[x],x]-y[x]==0,{y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{16} e^{-x} \left (4 x+9 e^{4 x/3}-9\right ) \]