2.329   ODE No. 329

\[ x^n y(x)^m \left (a x y'(x)+b y(x)\right )+\alpha x y'(x)+\beta y(x)=0 \]

✓ Mathematica : cpu = 1.23233 (sec), leaf count = 118

DSolve[beta*y[x] + alpha*x*Derivative[1][y][x] + x^n*y[x]^m*(b*y[x] + a*x*Derivative[1][y][x]) == 0,y[x],x]
 

\[\text {Solve}\left [\frac {m \left (n (a \beta -\alpha b) \log \left (x^n y(x)^m (b m-a n)-\alpha n+\beta m\right )+\beta (b m-a n) \log \left (n x^n (\alpha n-\beta m)\right )\right )}{n (a n-b m) (\alpha n-\beta m)}+\frac {\alpha m \log (\beta m y(x)-\alpha n y(x))}{\beta m-\alpha n}=c_1,y(x)\right ]\]

✓ Maple : cpu = 0.725 (sec), leaf count = 72

dsolve(y(x)^m*x^n*(a*x*diff(y(x),x)+b*y(x))+alpha*x*diff(y(x),x)+beta*y(x) = 0,y(x))
 

\[\left (x^{n} \left (a n -b m \right ) y \left (x \right )^{m}-\beta m +\alpha n \right )^{-m \left (a \beta -b \alpha \right )} \left (y \left (x \right )^{m}\right )^{\alpha \left (a n -b m \right )} x^{\beta m \left (a n -b m \right )}-c_{1} = 0\]