82.33.5 problem Ex. 5

Internal problem ID [18898]
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. 5
Date solved : Tuesday, January 28, 2025 at 12:33:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=x +{\mathrm e}^{m x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 70

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x+exp(m*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {36 c_{2} \left (m -2\right ) \left (m -3\right ) {\mathrm e}^{2 x}+36 c_{1} \left (m -2\right ) \left (m -3\right ) {\mathrm e}^{3 x}+36 \,{\mathrm e}^{m x}+\left (6 x +5\right ) m^{2}+\left (-30 x -25\right ) m +36 x +30}{36 m^{2}-180 m +216} \]

✓ Solution by Mathematica

Time used: 0.233 (sec). Leaf size: 58

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==x+Exp[m*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (m^2-5 m+6\right ) (6 x+5)+36 e^{m x}}{36 (m-3) (m-2)}+c_1 e^{2 x}+c_2 e^{3 x} \]