Internal problem ID [15466]
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 ODE’s). Section 17. Boundary value problems. Exercises page
163
Problem number: 722.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \left (-c_{3} +\left (x -1\right ) c_{4} \right ) \ln \left (x \right )+c_{3} \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 29
DSolve[{x^2*y''''[x]+4*x*y'''[x]+2*y''[x]==0,{y[1]==0,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (c_1-c_2) (x-1)+(c_2 x-c_1) \log (x) \]