Internal problem ID [11752]
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: 22.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$4)+6*diff(y(x),x$3)+15*diff(y(x),x$2)+20*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{4} {\mathrm e}^{-x} \cos \left (x \sqrt {2}\right )+c_{3} {\mathrm e}^{-x} \sin \left (x \sqrt {2}\right )+{\mathrm e}^{-2 x} \left (c_{2} x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 46
DSolve[y''''[x]+6*y'''[x]+15*y''[x]+20*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_4 x+c_2 e^x \cos \left (\sqrt {2} x\right )+c_1 e^x \sin \left (\sqrt {2} x\right )+c_3\right ) \]