Internal problem ID [12194]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 144.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+9*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} \sin \left (\sqrt {2}\, x \right )+c_{2} {\mathrm e}^{-x} \cos \left (\sqrt {2}\, x \right )+c_{3} {\mathrm e}^{x} \sin \left (\sqrt {2}\, x \right )+c_{4} {\mathrm e}^{x} \cos \left (\sqrt {2}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 52
DSolve[y''''[x]+2*y''[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (\left (c_4 e^{2 x}+c_2\right ) \cos \left (\sqrt {2} x\right )+\left (c_3 e^{2 x}+c_1\right ) \sin \left (\sqrt {2} x\right )\right ) \]