Internal problem ID [7761]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 181.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Riccati, _special]]
Solve \begin {gather*} \boxed {x^{4} \left (y^{\prime }+y^{2}\right )+a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 30
dsolve(x^4*(diff(y(x),x)+y(x)^2) + a=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\sqrt {a}\, \tan \left (\frac {\sqrt {a}\, \left (c_{1} x -1\right )}{x}\right )-x}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.251 (sec). Leaf size: 126
DSolve[x^4*(y'[x]+y[x]^2) + a==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (x+i \sqrt {-a} c_1\right ) \cos \left (\frac {\sqrt {a}}{x}\right )+\frac {\left (a-i \sqrt {-a} c_1 x\right ) \sin \left (\frac {\sqrt {a}}{x}\right )}{\sqrt {a}}}{x^2 \left (\cos \left (\frac {\sqrt {a}}{x}\right )-i c_1 \sinh \left (\frac {\sqrt {-a}}{x}\right )\right )} \\ y(x)\to \frac {x-\sqrt {a} \cot \left (\frac {\sqrt {a}}{x}\right )}{x^2} \\ \end{align*}