Internal problem ID [9101]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1522.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime } x^{4}-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 31
dsolve(4*x^4*diff(diff(diff(y(x),x),x),x)-4*x^3*diff(diff(y(x),x),x)+4*x^2*diff(y(x),x)-1=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} c_{1} \ln \relax (x )}{2}-\frac {c_{1} x^{2}}{4}+\frac {c_{2} x^{2}}{2}-\frac {1}{36 x}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 42
DSolve[-1 + 4*x^2*y'[x] - 4*x^3*y''[x] + 4*x^4*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} (2 c_1-c_2) x^2+\frac {1}{2} c_2 x^2 \log (x)-\frac {1}{36 x}+c_3 \\ \end{align*}