75.15.6 problem 437

Internal problem ID [16957]
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 : 437
Date solved : Tuesday, January 28, 2025 at 09:43:44 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)+6*diff(y(x),x$2)+11*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 27

DSolve[D[y[x],{x,3}]+6*D[y[x],{x,2}]+11*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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