40.8.2 problem 17

Internal problem ID [6702]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary problems. Page 86
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:24:26 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

\[ y = \left ({\mathrm e}^{3 x} c_2 +{\mathrm e}^{2 x} c_1 +c_3 \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 25

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

\[ y(x)\to -\frac {1}{2} c_1 e^{-2 x}+c_2 e^x+c_3 \]