HSC Science कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Solve the following differential equation:

`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`

Solve the following differential equation:

(e^y + 1)cos x dx + e^y sin x dy = 0

Solve the following differential equation:

`(ydx - xdy) cot (x/y)` = ny² dx

Solve the following differential equation:

`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0

Solve the following differential equation:

x cos y dy = e^x(x log x + 1) dx

Solve the following differential equation:

`tan y ("d"y)/("d"x) = cos(x + y) + cos(x - y)`

Solve the following differential equation:

`("d"y)/("d"x) = tan^2(x + y)`

Solve the following differential equation:

`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`

Solve the following differential equation:

`(x^3 + y^3)"d"y - x^2 y"d"x` = 0

Solve the following differential equation:

`y"e"^(x/y) "d"x = (x"e"^(x/y) + y) "d"y`

Solve the following differential equation:

`2xy"d"x + (x^2 + 2y^2)"d"y` = 0

Solve the following differential equation:

`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`

Solve the following differential equation:

`x ("d"y)/("d"x) = y - xcos^2(y/x)`

Solve the following differential equation:

`(1 + 3"e"^(y/x))"d"y + 3"e"^(y/x)(1 - y/x)"d"x` = 0, given that y = 0 when x = 1

Solve the following differential equation:

(x² + y²) dy = xy dx. It is given that y (1) = y(x₀) = e. Find the value of x₀

Choose the correct alternative:

The solution of `("d"y)/("d"x) + "p"(x)y = 0` is

Choose the correct alternative:

The general solution of the differential equation `log(("d"y)/("d"x)) = x + y` is

Choose the correct alternative:

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

Choose the correct alternative:

The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is

Choose the correct alternative:

If sin x is the integrating factor of the linear differential equation `("d"y)/("d"x) + "P"y = "Q"`, then P is