Solve 3e^xtan ydx +(1 + e^x)sec²ydy = 0 given y(0) = \(\frac { \pi }{ 4 } \)

Solve the differential equation y²dx + (xy + x²)dy = 0

If the marginal cost of producing x shoes is given by (3xy + y²)dx + (x² + xy)dy = 0 and the total cost of producing a pair of shoes is given by Rs. 12. Then find the total cost  function.

An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x² + y²)dy = xydx where x represents the number of units (in thousands). What is the total revenue function?

Solve the following differential equations (D²+D−6)y=e^3x + e^−3x