Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-1>Q 12

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The equation of the curve passing through origin and satisfying the differential equation $\frac{d y}{d x} = \sin (10 x + 6 y)$ 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-1>Q 13

Which one of the following curves represents the solution of the initial value problem

D y = 100 - y

where

y (0) = 50 ?

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-1>Q 14

A curve passing through

(2, 3)

and satisfying the differential equation

\int_{0}^{x} t y (t) d t = x^{2} y (x), (x > 0)

is

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-1>Q 15

A curve passes through the point

(1, \frac{π}{4})

and its slope at any point is given by

\frac{y}{x} - \cos^{2} (\frac{y}{x})

. Then, the curve has the equation

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-1>Q 16

The solution of the differential equation

(2 x - 10 y^{3}) \frac{d y}{d x} + y = 0

is

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-1>Q 17

Solution of differential equation

(1 + y^{2}) d x + (x - e^{\tan^{- 1} y}) d y = 0

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-1>Q 18

The general solution of the differential equation,

y^{'} + y ϕ^{'} (x) - ϕ (x) ϕ^{'} (x) = 0,

where

ϕ (x)

is a known function, is

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-1>Q 19

The solution of the differential equation,

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

with initial condition

y (0) = 0

, is

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Beta Question Bank for Engineering: Mathematics>Chapter 33 - Differential Equations>EXERCISE-1>Q 20

The solution of the differential equation

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

is