2.181   ODE No. 181

\[ a+x^4 \left (y'(x)+y(x)^2\right )=0 \]

✓ Mathematica : cpu = 0.127878 (sec), leaf count = 146

DSolve[a + x^4*(y[x]^2 + Derivative[1][y][x]) == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {-\frac {i e^{-\frac {i \sqrt {a}}{x}}}{2 \sqrt {a}}+\frac {e^{-\frac {i \sqrt {a}}{x}}}{2 x}+c_1 \left (e^{\frac {i \sqrt {a}}{x}}-\frac {i \sqrt {a} e^{\frac {i \sqrt {a}}{x}}}{x}\right )}{\frac {i x e^{-\frac {i \sqrt {a}}{x}}}{2 \sqrt {a}}-c_1 x e^{\frac {i \sqrt {a}}{x}}}\right \}\right \}\]

✓ Maple : cpu = 0.081 (sec), leaf count = 27

dsolve(x^4*(diff(y(x),x)+y(x)^2)+a = 0,y(x))
 

\[y \left (x \right ) = \frac {-\tan \left (\sqrt {a}\, \left (-\frac {1}{x}+c_{1} \right )\right ) \sqrt {a}+x}{x^{2}}\]