69.1.97 problem 144

Internal problem ID [14250]
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
Date solved : Tuesday, January 28, 2025 at 06:23:19 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+9*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{-x}+c_4 \,{\mathrm e}^{x}\right ) \cos \left (\sqrt {2}\, x \right )+\sin \left (\sqrt {2}\, x \right ) \left (c_{1} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{x}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 52

DSolve[D[y[x],{x,4}]+2*D[y[x],{x,2}]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\left (c_4 e^{2 x}+c_2\right ) \cos \left (\sqrt {2} x\right )+\left (c_3 e^{2 x}+c_1\right ) \sin \left (\sqrt {2} x\right )\right ) \]