Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment Set-2>Q 41

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Integrating factor of the equation $(x^{2} + 1) \frac{d y}{d x} + 2 x y = x^{2} - 1$ is

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Important Questions on Differential Equations

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment Set-2>Q 42

If

y (t)

is solution of

(1 + t) \frac{d y}{d t} - t y = 1

and

y (0) = - 1,

then

y (1)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment Set-2>Q 43

A differentiable function

y (x)

in

(0, π)

satisfying

y^{'} = 1 + y^{2}, y (0) = 0 = y (π)

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment Set-2>Q 44

The differential equation for which

\sin^{- 1} x + \sin^{- 1} y = 1

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment Set-2>Q 46

If

\int_{a}^{x} t y (t) d t = x^{2} + y (x)

, then

y (x) = λ - (λ + a^{2}) e^{\frac{x^{2} - a^{2}}{λ}}

, where

λ

is a natural number then

5^{λ}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment Set-2>Q 48

If the function

y = e^{4 x} + 2 e^{- x}

is a solution of the differential equation

\frac{d^{3} y}{d x^{3}} - 13 \frac{d y}{d x} - k y = 0

, then

k

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment Set-2>Q 50

The solution of

y^{4} d x + 2 x y^{3} d y = \frac{y d x - x d y}{x^{3} y^{3}}

is

x^{a} y^{b} + k \ln \frac{y}{x} =

constant, where

a, b

and

k

are natural numbers then

(a + b + k)

is

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment>Q 1

The differential equation of all ellipses centred at the origin having major and minor axes along coordinate axes is

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment>Q 2

The solution of differential equation

y d x + (x + x y) d y = 0

is