Verify that the function y = a cos x + b sin x, where a, b ∊ R is a solution of the differential equation $fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.$

Solution

$straight y space equals space straight a space cosx space plus space straight b space sinx$ ...(1)
$therefore space space space dy over dx space equals space minus straight a space sinx space plus space straight b space cosx rightwards double arrow space space space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space minus straight a space cosx space minus space straight b space sinx rightwards double arrow space space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space minus straight y space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space of space left parenthesis 1 right parenthesis close square brackets rightwards double arrow space fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0$
$therefore space space space straight y space equals space straight a space cosx space plus space straight b space sinx$ is a solution of the differential equation
$fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.$

For Daily Free Study Material Join wiredfaculty

Vector Algebra

Verify that the function y = a cos x + b sin x, where a, b ∊ R is a solution of the differential equation $fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.$

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Vector Algebra

Verify that the function y = a cos x + b sin x, where a, b ∊ R 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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Verify that the function y = a cos x + b sin x, where a, b ∊ R is a solution of the differential equation $fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.$

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