Internal problem ID [11774]
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: 46.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$4)+3*diff(y(x),x$3)+diff(y(x),x$2)+13*diff(y(x),x)+30*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{3} {\mathrm e}^{4 x} \sin \left (2 x \right )+c_{4} {\mathrm e}^{4 x} \cos \left (2 x \right )+c_{2} {\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 43
DSolve[y''''[x]+3*y'''[x]+y''[x]+13*y'[x]+30*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 e^x \cos (2 x)+e^{-3 x} \left (c_4 e^x+c_1 e^{4 x} \sin (2 x)+c_3\right ) \]