2.110   ODE No. 110

\[ f(x) \left (y(x)^2-x^2\right )+x y'(x)-y(x)=0 \]

✓ Mathematica : cpu = 0.0967685 (sec), leaf count = 56

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

\[\left \{\left \{y(x)\to -\frac {x \left (-1+\exp \left (2 \int _1^x-f(K[1])dK[1]+2 c_1\right )\right )}{1+\exp \left (2 \int _1^x-f(K[1])dK[1]+2 c_1\right )}\right \}\right \}\]

✓ Maple : cpu = 0.037 (sec), leaf count = 13

dsolve(x*diff(y(x),x)+f(x)*(y(x)^2-x^2)-y(x) = 0,y(x))
 

\[y \left (x \right ) = \tanh \left (\int f \left (x \right )d x +c_{1} \right ) x\]