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

Obtain the differential equations by eliminating arbitrary constants from the following equation.

`y = c_2 + c_1/x`

Obtain the differential equation by eliminating arbitrary constants from the following equations.

y = (c₁ + c₂ x) e^x

Obtain the differential equations by eliminating arbitrary constants from the following equations.

y = c₁e ^3x + c₂e ^2x

Obtain the differential equation by eliminating arbitrary constants from the following equation.

y² = (x + c)³

Find the differential equation by eliminating arbitrary constants from the relation x² + y² = 2ax

Form the differential equation by eliminating arbitrary constants from the relation

bx + ay = ab.

Find `"dy"/"dx"`if, y = `"x"^("x"^"2x")`

Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`

Solve the following differential equation.

(x² − yx² ) dy + (y² + xy²) dx = 0

Find `"dy"/"dx"`if, y = `"e"^("x"^"x")`

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

Find `"dy"/"dx"`if, y = (2x + 5)^x 

Find `"dy"/"dx"`if, y = `root(3)(("3x" - 1)/(("2x + 3")(5 - "x")^2))`

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

Find `dy/dx`if, y = `(x)^x + (a^x)`.

Find `"dy"/"dx"`if, y = `10^("x"^"x") + 10^("x"^10) + 10^(10^"x")`

If y = e^logx then `dy/dx` = ?

If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?` 

Fill in the Blank

If 0 = log(xy) + a, then `"dy"/"dx" =  (-"y")/square`

Fill in the blank.

If x = t log t and y = t^t, then `"dy"/"dx"` = ____