75.15.14 problem 445

Internal problem ID [16965]
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 : 445
Date solved : Tuesday, January 28, 2025 at 09:43:54 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

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

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