Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 29 - Differential Equations>Practice Exercise>Q 59

EASY

NDA & NA EE

IMPORTANT

Earn 100

What are the order and degree respectively of the differential equation whose solution is $y = c x + c^{2} - 3 c^{3 / 2} + 2,$ where $c$ is a parameter $?$

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Important Questions on Differential Equations

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 29 - Differential Equations>Practice Exercise>Q 1

The differential equation of the family of curves

y = A e^{3 x} + B e^{5 x},

where

A

and

B

are arbitrary constants, is

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 29 - Differential Equations>Practice Exercise>Q 3

Equation of the curve passing through

(3, 9)

which satisfies the differential equation

\frac{d y}{d x} = x + \frac{1}{x^{2}}

is

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 29 - Differential Equations>Practice Exercise>Q 4

The solution of the equation

\log_{e} (\frac{d y}{d x}) = a x + b y

is

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 29 - Differential Equations>Practice Exercise>Q 5

The solution of the equation

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

is

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 29 - Differential Equations>Practice Exercise>Q 6

The solution of the equation

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

is

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 29 - Differential Equations>Practice Exercise>Q 7

If $x \frac{d y}{d x} = y (\log y - \log x + 1),$ then the solution of the equation is

Note: Base of logarithm is assumed as $e$ .

HARD

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 29 - Differential Equations>Practice Exercise>Q 8

Solution of the differential equation

y_{3} - 8 y_{2} = 0

, where

y (0) = \frac{1}{8}, y_{1} (0) = 0, y_{2} (0) = 1

is equal to

HARD

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 29 - Differential Equations>Practice Exercise>Q 9

If

y + x \frac{d y}{d x} = x \frac{ϕ (x y)}{ϕ^{'} (x y)},

then

ϕ (x y)

is equal to