82.33.28 problem Ex. 28

Internal problem ID [18921]
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. 28
Date solved : Tuesday, January 28, 2025 at 12:37:06 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

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

\[ y \left (x \right ) = \left (c_3 x +c_{2} \right ) {\mathrm e}^{2 x}+{\mathrm e}^{-x} c_{1} +\frac {{\mathrm e}^{3 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 36

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

\[ y(x)\to \frac {e^{3 x}}{4}+c_1 e^{-x}+e^{2 x} (c_3 x+c_2) \]