82.33.27 problem Ex. 27

Internal problem ID [18920]
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. 27
Date solved : Tuesday, January 28, 2025 at 12:37:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+20 y&=20 x \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-9*diff(y(x),x)+20*y(x)=20*x,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{4 x} c_{2} +c_{1} {\mathrm e}^{5 x}+x +\frac {9}{20} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]-9*D[y[x],x]+20*y[x]==20*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+c_1 e^{4 x}+c_2 e^{5 x}+\frac {9}{20} \]