In the following, verify that the given functions, (explicit or implicit) is a solution of the corresponding differential equation:
$straight y space equals space square root of 1 plus straight x squared end root$ : $straight y apostrophe space equals space fraction numerator xy over denominator 1 plus straight x squared end fraction$

Solution

$straight y space equals space square root of 1 plus straight x squared end root$ ...(1)
$therefore$    $straight y apostrophe space equals space fraction numerator 2 straight x over denominator 2 square root of 1 plus straight y squared end root end fraction space space or space space space straight y apostrophe space equals space fraction numerator straight x over denominator square root of 1 plus straight x squared end root end fraction$ ...(2)
R.H.S. = $fraction numerator xy over denominator 1 plus straight x squared end fraction space equals space fraction numerator straight x square root of 1 plus straight x squared end root over denominator 1 plus straight x squared end fraction$    $open square brackets because space space of space space left parenthesis 1 right parenthesis close square brackets$
$equals space fraction numerator straight x over denominator square root of 1 plus straight x squared end root end fraction space equals straight y apostrophe$    $open square brackets because space of space left parenthesis 2 right parenthesis close square brackets$
$equals space straight L. straight H. straight S.$
$therefore space space space straight y space equals space square root of 1 plus straight x squared end root$ is a solution of $straight y apostrophe space equals space fraction numerator xy over denominator 1 plus straight x squared end fraction$

Some More Questions From Vector Algebra Chapter

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Vector Algebra

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:
y' + y = e^x

Determine order and degree (if defined) of differential equations:
y'' + (y')² + 2 y = 0

Determine order and degree (if defined) of differential equations:
y″ + 2y′ + sin y = 0

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NCERT Sample Papers

Entrance Exams Preparation

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Vector Algebra

In the following, verify that the given functions, (explicit or implicit) is a solution of the corresponding differential equation: :

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:y' + y = ex

Determine order and degree (if defined) of differential equations:y'' + (y')2 + 2 y = 0

Determine order and degree (if defined) of differential equations:y″ + 2y′ + sin y = 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Determine order and degree (if defined) of differential equations:
y' + y = e^x

Determine order and degree (if defined) of differential equations:
y'' + (y')² + 2 y = 0

Determine order and degree (if defined) of differential equations:
y″ + 2y′ + sin y = 0