Differential Calculus

2xydx + ( y^2 + x^2 ) dy = 0

[ 2x + y cos (x^2) - 2xy + 1 ] dx + [ sin (x^2) - x^2 ] dy = 0

Please help me again to solve this.

(e^2y-ycosxy)dx-y(1-x²)dy=0

How can we simplify ln(9m^2 n -mn^3) +x +y = c ?

3y-2yx^2 [ 1 + (ln (2x^3 / 3y^2))^2 ]dx - 2xdy =0

The topic is Additional Topics in Ordinary DE of the first order. Thank you so much.

3y-2yx^2 [ 1 + (ln (2x^3 / 3y^2))^2 ]dx - 2xdy =0

Bernoulli?

1- 3rss' + r^2 s^2 s' =0

Help me with this please.

The topic is Additional Topics in Ordinary DE of the first order.

y(3x^3 -x +y)dx + x^2(1-x^2)dy =0

Find the dimensions of the largest circular cone that can be inscribed in a sphere of radius R.

Find the ratio of the altitude h to the base radius r of a right circular cylinder having the largest lateral surface area S, if the right circular cylinder is to be inscribed in a sphere of radius R.