81.4.4 problem 4

Internal problem ID [18658]
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 : 4
Date solved : Tuesday, January 28, 2025 at 12:08:57 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(2*diff(y(x),x$3)+diff(y(x),x$2)-4*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left ({\mathrm e}^{\frac {5 x}{2}} c_{1} +c_3 x +c_{2} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

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

\[ y(x)\to e^{-x} \left (c_1 e^{5 x/2}+c_3 x+c_2\right ) \]