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Vector Algebra

Question

In the following, verify that the given functions, (explicit or implicit) is a solution of the corresponding differential equation:
$straight y space equals space straight e to the power of straight x plus 1$ : $straight y to the power of straight n minus straight y apostrophe space equals space 0$

Solution

y = e^x + 1 ;   ...(1)
∴ y' = e^x    ...(2)
and    y'' = e^x    ...(3)
L.H.S. = y'' – y'
= e^x – e^x    [∵ of (2), (3)]
= 0 = R.H.S.
∴ y = e^x + 1 is a solution of y'' – y' = 0

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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:
$straight y space equals space straight e to the power of straight x plus 1$ : $straight y to the power of straight n minus straight y apostrophe space equals space 0$

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In the following, verify that the given functions, (explicit or implicit) is a solution of the corresponding differential equation:
$straight y space equals space straight e to the power of straight x plus 1$ : $straight y to the power of straight n minus straight y apostrophe space equals space 0$

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