Question

यदि y = 5 cos x – 3 sin x है तो सिद्ध कीजिए कि
d^{2}y/dx^{2} +y =0

Answer 1

Given----> y = 5 Cosx - 3 Sinx

To prove----> d²y / dx² + y = 0

Proof----> We know that,

d/dx ( Sinx ) = Cosx

d/dx ( Cosx ) = - Sinx

Now, y = 5 Cosx - 3 Sinx

Differentiating with respect to x , we get,

=> dy/dx = d/dx ( 5Cosx ) - d/dx ( 3Sinx )

= 5 d/dx ( Cosx ) - 3 d/dx ( Sinx )

=> dy/dx = 5 ( - Sinx ) - 3 ( Cosx )

=> dy/dx = - 5 Sinx - 3 Cosx

Differentiating with respect to x again , we get,

=> d²y/dx² = -5 d/dx ( Sinx ) - 3 d/dx ( Cosx )

= - 5 Cosx - 3 ( - Sinx )

= - 5 Cosx + 3 Sinx

= - ( 5 Cosx - 3 Sinx )

=> d²y/dx² = - y

=> d²y/dx² + y = 0

Answer 2

d²y/dx²  + y = 0  यदि y = 5 cos x – 3 sin x

Step-by-step explanation:

द्वितीय कोटि के अवकलज ज्ञात कीजिए

y =  5 cos x – 3 sin x

=>  dy/dx =  5 (-Sinx) - 3(Cosx)

=>  dy/dx = - (5Sinx + 3Cosx)

d²y/dx²   =    - ( 5Cosx - 3Sinx)

=> d²y/dx²   =  - y

=> d²y/dx²  + y = 0

QED

सिद्ध

और अधिक जानें :

X^{20}  द्वितीय कोटि के अवकलज ज्ञात कीजिए

https://brainly.in/question/15287535

x cos x  द्वितीय कोटि के अवकलज ज्ञात कीजिए

https://brainly.in/question/15287541