64.10.21 problem 21

Internal problem ID [13427]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 05:42:16 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)-2*diff(y(x),x$2)+2*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{1} +{\mathrm e}^{2 x} c_{2} +c_{3} \sin \left (x \right ) {\mathrm e}^{-x}+c_4 \,{\mathrm e}^{-x} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 37

DSolve[D[y[x],{x,4}]-3*D[y[x],{x,3}]-2*D[y[x],{x,2}]+2*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{3 x} \left (c_4 e^x+c_3\right )+c_2 \cos (x)+c_1 \sin (x)\right ) \]