Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-1>Q 56

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The differential equation whose solution is ${(x - h)}^{2} + {(y - k)}^{2} = a^{2}$ ( $a$ is a constant), is

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Important Questions on Differential Equations

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Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-1>Q 57

If $\frac{d y}{d x} = e^{- 2 y}$ and $y = 0$ when $x = 5$ , then the value of $x$ when $y = 3$ is

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Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-1>Q 58

If

ϕ (x) = ϕ' (x)

and

ϕ (1) = 2,

then

ϕ (3)

equals

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Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-1>Q 59

If

\frac{d y}{d x} = 1 + x + y + x y

and

y (- 1) = 0,

then function

y

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-1>Q 60

The value of

\lim_{x \to \infty} y (x)

obtained from the differential equation

\frac{d y}{d x} = y - y^{2}

, where

y (0) = 2

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-1>Q 61

The solution of

\frac{d y}{d x} + \sqrt{(\frac{1 - y^{2}}{1 - x^{2}})} = 0

is:

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Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-1>Q 62

Integral curve satisfying

y' = \frac{x^{2} + y^{2}}{x^{2} - y^{2}}, y (1) = 2,

has the slope at the point

(1, 2)

of the curve, equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-1>Q 63

The solution of the differential equation

x d y - y d x = 0

represents

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Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-1>Q 64

The slope of a curve at any point is the reciprocal of twice the ordinate of the point and it passes through the point

(4, 3) .

The equation of the curve is