75.15.11 problem 442

Internal problem ID [16962]
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 : 442
Date solved : Tuesday, January 28, 2025 at 09:43:49 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(x),x$4)+4*diff(y(x),x$3)+10*diff(y(x),x$2)+12*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 32

DSolve[D[y[x],{x,4}]+4*D[y[x],{x,3}]+10*D[y[x],{x,2}]+12*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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