83.17.12 problem 12

Internal problem ID [19208]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Misc. Examples on chapter III at page 50
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 01:13:31 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 43

dsolve(diff(y(x),x$5)-13*diff(y(x),x$3)+26*diff(y(x),x$2)+82*diff(y(x),x)+104*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-4 x} \left (\left (\sin \left (x \right ) c_4 +c_5 \cos \left (x \right )\right ) {\mathrm e}^{3 x}+\left (\sin \left (2 x \right ) c_{2} +c_3 \cos \left (2 x \right )\right ) {\mathrm e}^{7 x}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 58

DSolve[D[y[x],{x,5}]-13*D[y[x],{x,3}]+26*D[y[x],{x,2}]+82*D[y[x],x]+104*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-4 x} \left (c_2 e^{3 x} \cos (x)+c_4 e^{7 x} \cos (2 x)+c_1 e^{3 x} \sin (x)+c_3 e^{7 x} \sin (2 x)+c_5\right ) \]