82.33.9 problem Ex. 9

Internal problem ID [18902]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 9
Date solved : Tuesday, January 28, 2025 at 12:34:02 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-13 y^{\prime }+12 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 41

dsolve(diff(y(x),x$3)-13*diff(y(x),x)+12*y(x)=x,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (144 c_3 \,{\mathrm e}^{7 x}+144 c_{1} {\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} x +13 \,{\mathrm e}^{4 x}+144 c_{2} \right ) {\mathrm e}^{-4 x}}{144} \]

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,3}]-13*D[y[x],x]+12*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x}{12}+c_1 e^{-4 x}+c_2 e^x+c_3 e^{3 x}+\frac {13}{144} \]