Internal problem ID [9097]
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]]
\[ \boxed {4 y^{\prime \prime \prime } x^{4}-4 x^{3} y^{\prime \prime }+4 y^{\prime } x^{2}-1=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{1} x^{2} \ln \left (x \right )}{2}-\frac {x^{2} c_{1}}{4}+\frac {c_{2} x^{2}}{2}-\frac {1}{36 x}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.011 (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*}