64.10.22 problem 22

Internal problem ID [13428]
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 : 22
Date solved : Tuesday, January 28, 2025 at 05:42:16 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 39

dsolve(diff(y(x),x$4)+6*diff(y(x),x$3)+15*diff(y(x),x$2)+20*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 46

DSolve[D[y[x],{x,4}]+6*D[y[x],{x,3}]+15*D[y[x],{x,2}]+20*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_4 x+c_2 e^x \cos \left (\sqrt {2} x\right )+c_1 e^x \sin \left (\sqrt {2} x\right )+c_3\right ) \]