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Differential Equation NAT Level - 1 - Question 1

If the Particular Integral (P.I.) of the differential equation (D^{3} + 1)y = cos^{2}x. is given by y = 1/65 (cos 2x - β sin 2x). Find the value of β

Detailed Solution for Differential Equation NAT Level - 1 - Question 1

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Differential Equation NAT Level - 1 - Question 2

I.F of differential equation (y^{2} + 2x^{2}y)dx + (2x^{3} – xy)dy = 0 is of the form x^{α}y^{β}. Then find value of α + β

Detailed Solution for Differential Equation NAT Level - 1 - Question 2

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Differential Equation NAT Level - 1 - Question 3

The IF for the Differential Equation (1 + xy)y + x (1 - xy)dy/dx = 0 is x^{α}y^{β}. Then find the value of the α + β.

Detailed Solution for Differential Equation NAT Level - 1 - Question 3

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Differential Equation NAT Level - 1 - Question 4

Find the value of f(0) where f(x) is the Particular Integral (P.I.) of the Differential equation (D^{2} –2D + 1)y = x sin x.

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Differential Equation NAT Level - 1 - Question 5

Solve In the solution find the value of constant which is in multiplication with cos x only given *y*(0) = 0.

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Differential Equation NAT Level - 1 - Question 6

Let y be a function of x satisfying dy/dx = 2x^{3} y(0) = 0**,** then find the value of e^{2}y(1).

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Differential Equation NAT Level - 1 - Question 7

Given a differential equation *y*(0) = 1, *y*(1) = *e*^{4}, then *y*(4) = e^{α} . Find the value of α.

Detailed Solution for Differential Equation NAT Level - 1 - Question 7

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Differential Equation NAT Level - 1 - Question 8

The Particular Integral (PI) of the differential equation (D^{2} – 5D + 6)y = x is given as y = mx + c. Find the value of c.

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Differential Equation NAT Level - 1 - Question 9

If the differential equation (3a^{2}y^{2}x^{2} + bycosx)dx + (2sinx – 4ayx^{3})dy = 0 is exact then what is the value of a, b ≠ 0.

Detailed Solution for Differential Equation NAT Level - 1 - Question 9

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Differential Equation NAT Level - 1 - Question 10

If the Particular Integral (PI) of the Differential equation (D^{2} + a^{2})y = cos ax is given by f(x). Then find the value of a^{2}f (π/2a).

Detailed Solution for Differential Equation NAT Level - 1 - Question 10

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