2.170   ODE No. 170

\[ -x^4+x^3 y'(x)-y(x)^2=0 \]

✓ Mathematica : cpu = 0.0641557 (sec), leaf count = 43

DSolve[-x^4 - y[x]^2 + x^3*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {x^3 \left (\frac {1}{x^2}-\frac {\log (x)}{x^2}-\frac {c_1}{x^2}\right )}{\frac {\log (x)}{x}+\frac {c_1}{x}}\right \}\right \}\]

✓ Maple : cpu = 0.017 (sec), leaf count = 23

dsolve(x^3*diff(y(x),x)-y(x)^2-x^4 = 0,y(x))
 

\[y \left (x \right ) = \frac {x^{2} \left (\ln \left (x \right )-c_{1} -1\right )}{\ln \left (x \right )-c_{1}}\]