Internal problem ID [11751]
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: 21.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)-2*diff(y(x),x$2)+2*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{3 x}+c_{3} {\mathrm e}^{-x} \sin \left (x \right )+c_{4} {\mathrm e}^{-x} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 37
DSolve[y''''[x]-3*y'''[x]-2*y''[x]+2*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (e^{3 x} \left (c_4 e^x+c_3\right )+c_2 \cos (x)+c_1 \sin (x)\right ) \]