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If y=x^(n-1) log x, prove that (x^2y2)+...

If ` y=x^(n-1) log x`, prove that `(x^2y_2)+(3-2n)xy_1+(n-1)^2`.y=0 where` y_1=dy/dx and y_2=(d^2)/(dx^2)`.

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A DAS GUPTA-Differentiation-Exercise
  1. If y=sin(2sin^-1x)show that (1-x^2)(d^2y)/(dx^2)= xdy/dx-4y

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  2. If y=a cos (logx)+b sin (logx), prove that x^(2)y(2)+xy(1)+y=0.

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  3. If y=x^(n-1) log x, prove that (x^2y2)+(3-2n)xy1+(n-1)^2.y=0 where y1...

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  4. Let y=tan^-1sqrt(x^2-1). Prove that (2x^2-1)((dy)/(dx))+x(x^2-1)((d^2...

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  5. If y=(a x+b)/(x^2+c), prove that (2x y1+y)y3=3(x y2+y1)y2.

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  6. Let y=f(x).phi(x) and z=f'(x).phi'(x). prove that 1/y*(d^2y)/(dx^2)=1/...

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  7. Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)...

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  8. Let f'(x) exists for all x != 0 and f(xy) = f(x) + f(y) for all real x...

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  16. Let f(x) be a function satisfying the condition f(-x) = f(x) for all r...

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  18. Find the sum of series sum(r=1)^nr.x^(r-1), using calculus.

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  19. Differential coefficient of log2(log2x)w.r.t x is

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  20. If f(x)=logx(logex) then f'(e)=

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