81.5.10 problem 10

Internal problem ID [18673]
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 58
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 12:09:13 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

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

\[ y \left (x \right ) = -\frac {\left (\left (x -1\right ) {\mathrm e}^{2 x}-4 c_{2} {\mathrm e}^{x}-4 c_3 \,{\mathrm e}^{4 x}-4 c_{1} \right ) {\mathrm e}^{-2 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 38

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

\[ y(x)\to -\frac {x}{4}+c_1 e^{-2 x}+c_2 e^{-x}+c_3 e^{2 x}+\frac {1}{4} \]