81.4.6 problem 6

Internal problem ID [18660]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 48
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 12:08:58 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+diff(y(x),x)-5*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left ({\mathrm e}^{3 x} c_{1} +\sin \left (x \right ) c_{2} +c_3 \cos \left (x \right )\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

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

\[ y(x)\to e^{-2 x} \left (c_3 e^{3 x}+c_2 \cos (x)+c_1 \sin (x)\right ) \]