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

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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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Important Questions on Differential Equations

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment>Q 3

The solution of

\frac{d y}{d x} = \frac{a x + h}{b y + k}

represents a parabola when

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment>Q 4

If

y = y (x)

and

\frac{2 + \sin x}{y + 1} (\frac{d y}{d x}) = - \cos x, y (0) = 1,

then

y (\frac{π}{2}) =

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment>Q 5

The real value of

n

for which substitution

y = u^{n}

will transform differential equation

2 x^{4} y \frac{d y}{d x} + y^{4} = 4 x^{6}

, into a homogeneous equation

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment>Q 6

A particle starts at the origin and moves along the

x

-axis in such a way that its velocity at the point

(x, 0)

is given by the formula

\frac{d x}{d t} = \cos^{2} π x

. Then, the particle never reaches the point on

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Gamma Question Bank for Engineering Mathematics>Chapter 30 - Differential Equations>Assignment>Q 7

Solve

(1 + e^{\frac{x}{y}}) d x + e^{\frac{x}{y}} (1 - \frac{x}{y}) d y = 0