Internal problem ID [6359]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED
HARMONIC OSCILLATORS Page 98
Problem number: 12.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)-2*diff(y(x),x$2)-6*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{x} x +c_{3} {\mathrm e}^{-2 x} \sin \left (x \right )+c_{4} {\mathrm e}^{-2 x} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 35
DSolve[y''''[x]+2*y'''[x]-2*y''[x]-6*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (e^{3 x} (c_4 x+c_3)+c_2 \cos (x)+c_1 \sin (x)\right ) \]