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Differential Equation NAT Level - 2 - Question 1

Find the orthogonal trajectory of the family of curves, y^{2} = x^{3} – 2 so, find the value of y as x → ∞.

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

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Differential Equation NAT Level - 2 - Question 2

If the P.I. of the Differential Equation is of the value form Find the value of λ.

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

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Differential Equation NAT Level - 2 - Question 3

If the solution of is of the y^{2} = a_{1}x + a_{2}x^{α}. Find the value of α.

Detailed Solution for Differential Equation NAT Level - 2 - Question 3

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Differential Equation NAT Level - 2 - Question 4

If e^{x} and x are solutions of Homogeneous equations (1 – x)y_{2} + xy_{1} – y = 2(x – 1)^{2}e^{–x} then the general solution y is of the form y = c_{1}x + c_{2}e^{x} + α - xe^{-x}. Find the value of α.

Detailed Solution for Differential Equation NAT Level - 2 - Question 4

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Differential Equation NAT Level - 2 - Question 5

Find the order of differential equation of all tangents to parabola y^{2} = x

Detailed Solution for Differential Equation NAT Level - 2 - Question 5

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Differential Equation NAT Level - 2 - Question 6

If the P.I. of the differential equation (D^{2} – 1)y = coshxcosx is of the form α.(2 sin hx sin x - cosx).

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Differential Equation NAT Level - 2 - Question 7

An integrating factor of the equation dy/dx + x sin 2y = x^{3} cos^{2} y is f(x). Find the value of f(0).

Detailed Solution for Differential Equation NAT Level - 2 - Question 7

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Differential Equation NAT Level - 2 - Question 8

If the PI of differential equation (D^{2} - 4D + 4) y = 8x^{2}e^{2}x sin 2x is of the form e^{αx} [(α'x^{2} + α") sin βx + β' x cos βx] then find the value of α".

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Differential Equation NAT Level - 2 - Question 9

If the integrating factor of the differential equation (x^{7}y^{2} + 3y)dx + (3x^{8}t - x)dy = 0 is of the form x^{m}y^{n} then sum of values of m and n is :

Detailed Solution for Differential Equation NAT Level - 2 - Question 9

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Differential Equation NAT Level - 2 - Question 10

If the P.I. of Differential Equation (x^{2}D^{2} + 3xD + 1) y = 1/(1 - x)_{2} is of form then, find value of λ.

Detailed Solution for Differential Equation NAT Level - 2 - Question 10

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