HSC Science (Computer Science) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`

Integrate the following w.r.t.x:

`x^2/((x - 1)(3x - 1)(3x - 2)`

Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`

Integrate the following w.r.t.x :  `sec^2x sqrt(7 + 2 tan x - tan^2 x)`

Integrate the following w.r.t.x: `(x + 5)/(x^3 + 3x^2 - x - 3)`

Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`

Solve the following differential equation:

`dy/dx + y/x = x^3 - 3`

Solve the following differential equation:

`cos^2 "x" * "dy"/"dx" + "y" = tan "x"`

Solve the following differential equation:

`("x" + 2"y"^3) "dy"/"dx" = "y"`

Solve the following differential equation:

`"dy"/"dx" + "y" * sec "x" = tan "x"`

Solve the following differential equation:

`"x" "dy"/"dx" + "2y" = "x"^2 * log "x"`

Solve the following differential equation:

`("x + y") "dy"/"dx" = 1`

Solve the following differential equation:

`("x + a")"dy"/"dx" - 3"y" = ("x + a")^5`

Solve the following differential equation:

dr + (2r cotθ + sin2θ)dθ = 0

Solve the following differential equation:

y dx + (x - y²) dy = 0

Solve the following differential equation:

`(1 - "x"^2) "dy"/"dx" + "2xy" = "x"(1 - "x"^2)^(1/2)`

Solve the following differential equation:

`(1 + "x"^2) "dy"/"dx" + "y" = "e"^(tan^-1 "x")`

Find the equation of the curve which passes through the origin and has the slope x + 3y - 1 at any point (x, y) on it.

Find the equation of the curve passing through the point `(3/sqrt2, sqrt2)` having a slope of the tangent to the curve at any point (x, y) is -`"4x"/"9y"`.

The curve passes through the point (0, 2). The sum of the coordinates of any point on the curve exceeds the slope of the tangent to the curve at any point by 5. Find the equation of the curve.