Internal problem ID [10019]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1688 (book 6.97).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime } x^{4}-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 21
dsolve(x^4*diff(diff(y(x),x),x)-x*(x^2+2*y(x))*diff(y(x),x)+4*y(x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{2} \left (c_{1} \tanh \left (c_{1} \left (-\ln \left (x \right )+c_{2} \right )\right )+1\right ) \]
✓ Solution by Mathematica
Time used: 79.662 (sec). Leaf size: 83
DSolve[4*y[x]^2 - x*(x^2 + 2*y[x])*y'[x] + x^4*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2 \left (\left (1-i \sqrt {-1-c_1}\right ) x^{2 i \sqrt {-1-c_1}}+\left (1+i \sqrt {-1-c_1}\right ) c_2\right )}{x^{2 i \sqrt {-1-c_1}}+c_2} \]