Internal problem ID [11744]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \left (\left (c_{3} x +c_{2} \right ) {\mathrm e}^{\frac {5 x}{2}}+c_{1} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 93
DSolve[4*y'''[x]+4*y''[x]+7*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3+4 \text {$\#$1}^2+7 \text {$\#$1}+2\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3+4 \text {$\#$1}^2+7 \text {$\#$1}+2\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3+4 \text {$\#$1}^2+7 \text {$\#$1}+2\&,3\right ]\right ) \]