Home
Class 12
MATHS
Verify that the given functions (explic...

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:`y = x sin x` : `x yprime=y+xsqrt(x^2-y^2)(x!=0`and`x > y or x < y`)

Text Solution

Verified by Experts

Given,
`=>y=xsinx and xy'=y+xsqrt(x^2−y^2)`
putting value of y in L.H.S `=>x*(xcosx+sinx)`
`=>x^2cosx+xsinx`
From R.H.S
`=>xsinx+xsqrt(x^2-(xsinx)^2)`
`=>xsinx-x**xsqrt(1-(sinx)^2)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: y=xsinx \ -> \ x y^(prime)=y+x\ sqrt(x^2-y^2)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : y=Ax : xy'=y(x ne 0)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=x^2+2x+C : yprime-2x-2=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=cosx+C : yprime+sinx=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=cosx+C : yprime+sinx=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=e^x+1:yprimeprime-yprime=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=e^x+1:yprimeprime-yprime=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=sqrt(1+x^2) : yprime=(x y)/(1+x^2)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=sqrt(1+x^2) : yprime=(x y)/(1+x^2)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=sqrt(1+x^2) : yprime=(x y)/(1+x^2)