75.22.18 problem 723

Internal problem ID [17197]
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 : 723
Date solved : Tuesday, January 28, 2025 at 09:56:55 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x 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: 0.026 (sec). Leaf size: 27

dsolve([x^3*diff(y(x),x$4)+6*x^2*diff(y(x),x$3)+6*x*diff(y(x),x$2)=0,y(1) = 0, D(y)(1) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 34

DSolve[{x^3*D[y[x],{x,4}]+6*x^2*D[y[x],{x,3}]+6*x*D[y[x],{x,2}]==0,{y[1]==0,Derivative[1][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {(x-1) (c_1 (x-1)+2 c_2 x)}{2 x}-c_2 \log (x) \]