75.15.15 problem 446

Internal problem ID [16966]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 446
Date solved : Tuesday, January 28, 2025 at 09:43:55 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

dsolve(diff(y(x),x$5)+4*diff(y(x),x$4)+5*diff(y(x),x$3)-6*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{3} {\mathrm e}^{3 x}+\left (c_4 \sin \left (x \right )+c_5 \cos \left (x \right )+c_{1} \right ) {\mathrm e}^{x}+c_{2} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 44

DSolve[D[y[x],{x,5}]+4*D[y[x],{x,4}]+5*D[y[x],{x,3}]-6*D[y[x],x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_4 e^x+c_5 e^{3 x}+c_2 e^x \cos (x)+c_1 e^x \sin (x)+c_3\right ) \]