77.1.125 problem 152 (page 224)

Internal problem ID [18015]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 152 (page 224)
Date solved : Tuesday, January 28, 2025 at 11:19:59 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 36

dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)+3*diff(y(x),x$2)+2*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,4}]+2*D[y[x],{x,3}]+3*D[y[x],{x,2}]+2*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/2} \left ((c_4 x+c_3) \cos \left (\frac {\sqrt {3} x}{2}\right )+(c_2 x+c_1) \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]