finding dy dx

If the differential equation is of the form M dx + N dy = 0, then the condition for exactness is _____. => ∂ M ∂ y = ∂ N ∂ x or ∂ M ∂ y = ∂ N ∂ y or ∂ M ∂ y ≠ ∂ N ∂ x or ∂ M ∂ y + ∂ N ∂ x = 0 or &..

Solve the differential equation ( x + y 2 ) dx + (2 xy + 1) dy = 0. => IV or III or I or II or V..

Solve the differential equation (2 x + y + 1) dx + (2 y + x + 2) dy = 0. => IV or III or V or II or I..

Solve x (1 + y 2 ) dx + y (1 + x 2 ) dy = 0. => I or III or II or V or IV..

Choose the correct statement(s) for the differential equation M dx + N dy = 0, where M = ( x 2 + 2 x + y ) and N = ( x 2 + 4 y - 2). => III and V only or II only or I only or IV only or I and II only..

Solve the differential equation ( y 2 - 2 xy ) dx + (2 xy - x 2 ) dy = 0. => xy 2 - x 2 y 2 = c or xy 2 - x 2 y = c or xy 2 + x 2 y = c or xy 2 - xy..

Conclusion - In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of dy/dx to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curve..

Express the differential equation in the form f(x) dx = g(y) dy..

Rate of Change of Quantity - If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to x For x = x 0 , dy/dx at x 0 is called the rate of change of y with respect ..

Let (dy/dx) (x1,y1) = m be the slope of the tangent at (x1, y1) on the curve y=f(x). 1. Equation of the tangent at (x 1 ,y 1 ) is 2. Equation of the normal at (x 1 ,y 1 ) is..