64.10.14 problem 14

Internal problem ID [13420]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 05:42:13 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(4*diff(y(x),x$3)+4*diff(y(x),x$2)-7*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 93

DSolve[4*D[y[x],{x,3}]+4*D[y[x],{x,2}]+7*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3+4 \text {$\#$1}^2+7 \text {$\#$1}+2\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3+4 \text {$\#$1}^2+7 \text {$\#$1}+2\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3+4 \text {$\#$1}^2+7 \text {$\#$1}+2\&,3\right ]\right ) \]