81.5.6 problem 6

Internal problem ID [18669]
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 : 6
Date solved : Tuesday, January 28, 2025 at 12:09:06 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=x,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {x}{6}-\frac {11}{36}+{\mathrm e}^{x} c_{1} +{\mathrm e}^{2 x} c_{2} +c_3 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x}{6}+c_1 e^x+c_2 e^{2 x}+c_3 e^{3 x}-\frac {11}{36} \]