75.22.17 problem 722

Internal problem ID [17196]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 17. Boundary value problems. Exercises page 163
Problem number : 722
Date solved : Tuesday, January 28, 2025 at 09:56:54 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 22

dsolve([x^2*diff(y(x),x$4)+4*x*diff(y(x),x$3)+2*diff(y(x),x$2)=0,y(1) = 0, D(y)(1) = 0],y(x), singsol=all)
 

\[ y = \left (-c_{3} +\left (x -1\right ) c_4 \right ) \ln \left (x \right )+c_{3} \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 29

DSolve[{x^2*D[y[x],{x,4}]+4*x*D[y[x],{x,3}]+2*D[y[x],{x,2}]==0,{y[1]==0,Derivative[1][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_1-c_2) (x-1)+(c_2 x-c_1) \log (x) \]