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If y+d/(dx)(x y)=x(sinx+logx),fin dy(x)d...

If `y+d/(dx)(x y)=x(sinx+logx),fin dy(x)dot`

Text Solution

Verified by Experts

The correct Answer is:
`y=- cos x + (2sinx)/(x)+(2cos x)/(x^(2))+(x log x)/(3)-x/9+cx^(-2)`.
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If y+d/(dx)(xy)=x(sinx+logx) , find y(x) .

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Knowledge Check

  • If (d)/(dx)((x)/(sinx))=

    A
    `cscx(1+xcotx)`
    B
    `cscx(xcotx-1)`
    C
    `cscx(1-xcotx)`
    D
    `cscx(1+xcosx)`

  • (d)/(dx)((logx)/(x^(2)))=

    A
    `x^(-2)(1+2logx)`
    B
    `x^(-2)(2logx-1)`
    C
    `x^(-3)(1-2logx)`
    D
    `x^(-4)(1-2logx)`

  • The solution of the differential equation x sin d (dy)/(dx) + ( x cos x + sin x ) y = sinx . When y (0)=0 is

    A
    ` xy sin x = 1- cos x `
    B
    `xy sin x + cos x =0`
    C
    `x sin x + y cos x =0`
    D
    `x sin x + y cos x =1 `

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    Find differentiation of y w.r.t x. (i) y=(sin x)/x , (ii) y=(4x^(3))/e^(x)

    (i) The degree of the differential equation (d^(2)y)/(dx^(2))+e^(dy//dx)=0 is… (ii) The degree of the differential equation sqrt(1+((dy)/(dx))^(2))="x is"....... (iii) The number of arbitrary constant in the general solution of differential equation of order three is.. (iv) (dy)/(dx)+(y)/(x log x)=(1)/(x) is an equation of the type.... (v) General solution of the differential equation of the type is givven by... (vi) The solution of the differential (xdy)/(dx)+2y=x^(2) is.... (vii) The solution of (1+x^(2))(dy)/(dx)+2xy-4xy^(2)=0 is... (viii) The solution of the differential equation ydx+(x+y)dy=0 is .... (ix) Genergal solution of (dy)/dx)+y=sin x is.... (x) The solution of differential equation cot y dx=xdy is.... (xi) The integrating factor of (dy)/(dx)+y=(1+y)/(x) is.....

    If y=f(x) is a differentiable function x such that invrse function x=f^(-1) y exists, then prove that x is a differentiable function of y and (dx)/(dy)=(1)/((dy)/(dx)) where (dy)/(dx) ne0 Hence, find (d)/(dx)(tan^(-1)x) .

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