HSC Commerce (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find `"dy"/"dx"` if, y = log(ax² + bx + c) 

Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`

Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`

Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`

Find the differential equation whose general solution is

x³ + y³ = 35ax.

Form the differential equation from the relation x² + 4y² = 4b²

Solve the following differential equation.

`dy/dx = x^2 y + y`

Solve the following differential equation.

`(dθ)/dt  = − k (θ − θ_0)`

Solve the following differential equation.

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

For each of the following differential equations find the particular solution.

(x − y² x) dx − (y + x² y) dy = 0, when x = 2, y = 0

For the following differential equation find the particular solution.

`(x + 1) dy/dx − 1 = 2e^(−y)`,

when y = 0, x = 1

Choose the correct alternative.

If y = (5x³ - 4x² - 8x)⁹, then `"dy"/"dx"` =

Choose the correct alternative.

If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`

If y = 2x² + 2² + a², then `"dy"/"dx" = ?`

Fill in the Blank.

If 3x²y + 3xy² = 0, then `(dy)/(dx)` = ______.

If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`

For each of the following differential equations find the particular solution.

`y (1 + logx)dx/dy - x log x = 0`,

when x=e, y = e².

For  the following differential equation find the particular solution.

`dy/ dx = (4x + y + 1),

when  y = 1, x = 0

Solve the following differential equation.

xdx + 2y dx = 0

The derivative of f(x) = a^x, where a is constant is x.a^x-1.