75.15.8 problem 439

Internal problem ID [16959]
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 : 439
Date solved : Tuesday, January 28, 2025 at 09:43:46 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(diff(y(x),x$6)+2*diff(y(x),x$5)+diff(y(x),x$4)=0,y(x), singsol=all)
 

\[ y = \left (x c_6 +c_5 \right ) {\mathrm e}^{-x}+c_4 \,x^{3}+x^{2} c_{3} +c_{2} x +c_{1} \]

✓ Solution by Mathematica

Time used: 41.775 (sec). Leaf size: 175

DSolve[D[y[x],{x,6}]+2*D[y[x],{x,5}]+D[y[x],{x,4}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \int _1^x\int _1^{K[4]}\int _1^{K[3]}\int _1^{K[2]}e^{-K[1]} (c_1+c_2 K[1])dK[1]dK[2]dK[3]dK[4]+x (x (c_6 x+c_5)+c_4)+c_3 \\ y(x)\to \frac {c_1 \left (x^3-6 x^2+15 x-16\right )}{6 e}+c_1 e^{-x}+x (x (c_6 x+c_5)+c_4)+c_3 \\ y(x)\to \frac {c_2 \left (2 x^3-15 x^2+48 x-65\right )}{6 e}+c_2 e^{-x} (x+4)+x (x (c_6 x+c_5)+c_4)+c_3 \\ \end{align*}