35.8.22 problem 22

Internal problem ID [6229]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 22
Date solved : Monday, January 27, 2025 at 01:49:28 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)+13*diff(y(x),x$2)-18*diff(y(x),x)+36*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 48

DSolve[D[y[x],{x,4}]-2*D[y[x],{x,3}]+13*D[y[x],{x,2}]-18*D[y[x],x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 \cos (3 x)+c_2 e^x \cos \left (\sqrt {3} x\right )+c_4 \sin (3 x)+c_1 e^x \sin \left (\sqrt {3} x\right ) \]