Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-2>Q 14

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The number of straight lines which satisfy the differential equation $\frac{d y}{d x} + x {(\frac{d y}{d x})}^{2} - y = 0$ , is

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Important Questions on Differential Equations

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-2>Q 15

Let

y = (A + B x) e^{3 x}

be a solution of the differential equation

\frac{d^{2} y}{d x^{2}} + m \frac{d y}{d x} + n y = 0, m, n \in I

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-2>Q 16

The differential equation

2 x y d y = (x^{2} + y^{2} + 1) d x

determines

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-2>Q 17

If

f^{''} (x) + f^{'} (x) + f^{2} (x) = x^{2}

be the differential equation of a curve and let

P

be the point of maxima then number of tangents which can be drawn from point

P

to

x^{2} - y^{2} = a^{2}, a \neq 0

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-2>Q 18

The solution of

x^{2} d y - y^{2} d x + x y^{2} (x - y) d y = 0

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-2>Q 19

The orthogonal trajectories of the system of curves

{(\frac{d y}{d x})}^{2} = \frac{4}{x}

are -

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-2>Q 20

The value of the constant

' m'

and

' c'

for which

y = m x + c

is a solution of the differential equation

D^{2} y - 3 D y - 4 y = - 4 x

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-2>Q 21

If

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

, then the solution of the equation is -

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-2>Q 22

Solutions of the differential equation

x^{2} {(\frac{d y}{d x})}^{2} + x y (\frac{d y}{d x}) - 6 y^{2} = 0