11.2.7 problem 14

Internal problem ID [1478]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.2, Higher order linear differential equations. Constant coefficients. page 180
Problem number : 14
Date solved : Monday, January 27, 2025 at 04:57:48 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(diff(y(x),x$5)-3*diff(y(x),x$4)+3*diff(y(x),x$3)-3*diff(y(x),x$2)+2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_1 +c_2 \,{\mathrm e}^{x}+c_3 \,{\mathrm e}^{2 x}+c_4 \sin \left (x \right )+c_5 \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 36

DSolve[D[y[x],{x,5}]-3*D[y[x],{x,4}]+3*D[y[x],{x,3}]-3*D[y[x],{x,2}]+2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^x+\frac {1}{2} c_4 e^{2 x}-c_2 \cos (x)+c_1 \sin (x)+c_5 \]