71.10.7 problem 7

Internal problem ID [14502]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 06:42:42 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(36*diff(y(x),x$4)-12*diff(y(x),x$3)-11*diff(y(x),x$2)+2*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = \left (\left (c_4 x +c_{3} \right ) {\mathrm e}^{\frac {5 x}{6}}+c_{2} x +c_{1} \right ) {\mathrm e}^{-\frac {x}{3}} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 41

DSolve[36*D[y[x],{x,4}]-12*D[y[x],{x,3}]-11*D[y[x],{x,2}]+2*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/3} \left (c_3 e^{5 x/6}+x \left (c_4 e^{5 x/6}+c_2\right )+c_1\right ) \]