82.25.1 problem Ex. 1

Internal problem ID [18871]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 66
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:33:10 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 27

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{3 x} (c_3 x+c_2)+c_1\right ) \]