Question

Verify that the function y = e^–3x is a solution of the differential equation $fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx minus 6 straight y space equals space 0$

Solution

$straight y space equals space straight e to the power of negative 3 straight x end exponent$ ...(1)
$therefore$ $dy over dx space equals space straight e to the power of negative 3 straight x end exponent. space left parenthesis negative 3 right parenthesis space space space space space space space or space space space space space dy over dx equals negative 3 straight e to the power of negative 3 straight x end exponent$ ...(2)
$fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative 3 space straight e to the power of negative 3 straight x end exponent. space left parenthesis negative 3 right parenthesis space space space or space space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space 9 straight e to the power of negative 3 straight x end exponent$ ...(3)
L.H.S. = $fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx minus 6 straight y space equals space 9 straight e to the power of negative 3 straight x end exponent minus 3 straight e to the power of 3 straight x end exponent minus 6 straight e to the power of negative 3 straight x end exponent space space space space space open square brackets because space of space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis comma space left parenthesis 3 right parenthesis close square brackets$
= 0 - R.H.S.
$therefore space space space straight y space equals straight e to the power of negative 3 straight x end exponent$ is a solution of the differential equation
$fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx minus 6 straight y space equals space 0$

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Vector Algebra

Verify that the function y = e^–3x is a solution of the differential equation $fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx minus 6 straight y space equals space 0$

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

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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For Daily Free Study Material Join wiredfaculty

Vector Algebra

Verify that the function y = e–3x is a solution of the 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

Verify that the function y = e^–3x is a solution of the differential equation $fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx minus 6 straight y space equals space 0$

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

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