73.17.13 problem 13

Internal problem ID [15547]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 08:01:46 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(diff(y(x),x$5)-6*diff(y(x),x$4)+13*diff(y(x),x$3)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 60.112 (sec). Leaf size: 64

DSolve[D[y[x],{x,5}]-6*D[y[x],{x,4}]+13*D[y[x],{x,3}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\int _1^{K[3]}\int _1^{K[2]}e^{3 K[1]} (c_2 \cos (2 K[1])+c_1 \sin (2 K[1]))dK[1]dK[2]dK[3]+x (c_5 x+c_4)+c_3 \]