Internal problem ID [8517]
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]]
\[ \boxed {x^{4} \left (y^{\prime }+y^{2}\right )=-a} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(x^4*(diff(y(x),x)+y(x)^2) + a=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\tan \left (\sqrt {a}\, \left (-\frac {1}{x}+c_{1} \right )\right ) \sqrt {a}-x}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.36 (sec). Leaf size: 111
DSolve[x^4*(y'[x]+y[x]^2) + a==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2 i a c_1 e^{\frac {2 i \sqrt {a}}{x}}+\sqrt {a} \left (1+2 c_1 x e^{\frac {2 i \sqrt {a}}{x}}\right )-i x}{x^2 \left (2 \sqrt {a} c_1 e^{\frac {2 i \sqrt {a}}{x}}-i\right )} y(x)\to \frac {x-i \sqrt {a}}{x^2} \end{align*}