Internal problem ID [11750]
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: 20.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x$4)-diff(y(x),x$3)-3*diff(y(x),x$2)+diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{4} x +c_{3} \right ) {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 33
DSolve[y''''[x]-y'''[x]-3*y''[x]+y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (c_2 x+e^{2 x} \left (c_4 e^x+c_3\right )+c_1\right ) \]