Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.

Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.

The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.

The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.

y = ae^mx+ be^–mx satisfies which of the following differential equation?

The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.

The solution of `x ("d"y)/("d"x) + y` = e^x is ______.

The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is ______.

The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.

The solution of the equation (2y – 1)dx – (2x + 3)dy = 0 is ______.

The differential equation for which y = acosx + bsinx is a solution, is ______.

The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.

Which of the following is the general solution of `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + y` = 0?

If k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.

General solution of `("d"y)/("d"x) + ytanx = secx` is ______.

Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.

The general solution of the differential equation (e^x + 1) ydy = (y + 1) e^xdx is ______.

The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.

The solution of the differential equation `("d"y)/("d"x) + (2xy)/(1 + x^2) = 1/(1 + x^2)^2` is ______.

The number of arbitrary constants in the general solution of a differential equation of order three is ______.