HSC Commerce Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Solve the following:

`x ("d"y)/("d"x) + 2y = x^4`

Solve the following:

`("d"y)/("d"x) + (3x^2)/(1 + x^3) y = (1 + x^2)/(1 + x^3)`

Solve the following:

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

Solve the following:

`("d"y)/("d"x) + y tan x = cos^3x`

Solve the following:

If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x.

Solve the following:

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

Solve the following:

A bank pays interest by continuous compounding, that is by treating the interest rate as the instantaneous rate of change of principal. A man invests ₹ 1,00,000 in the bank deposit which accrues interest, 8% per year compounded continuously. How much will he get after 10 years? (e^0.8 = 2.2255)

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If y = ex + c – c³ then its differential equation is

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The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is

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The differential equation of y = mx + c is (m and c are arbitrary constants)

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Solution of `("d"x)/("d"y) + "P"x = 0`

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If sec² x is an integrating factor of the differential equation `("d"y)/("d"x) + "P"y` = Q then P = 

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The solution of the differential equation `("d"y)/("d"x) + "P"y` = Q where P and Q are the function of x is

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The differential equation of x² + y² = a²

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A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution

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A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution

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The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is

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Which of the following is the homogeneous differential equation?

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

Form the differential equation having for its general solution y = ax² + bx