(i) If y=asin(log x) then prove that x^(...

(i) If `y=asin(log x)` then prove that `x^(2)(d^2y)/(dx^2)+x(dy)/(dx)+y=0`. (ii) If `y=acos(log_(e)x)+bsin(log_(e)x)`, then prove that `x^2y_2^2+x*y_(1)+y=0`.

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If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0
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(i) If y=asin(log x) then prove that x^(2)*(d^2y)/(dx^2)+x(dy)/(dx)+y=...
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If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2...
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If y=sin(sinx) then prove that (d^2y)/(dx^2)+tanx. (dy)/(dx)+y cos^2...
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IF y=e^(tan^(-1)x) then prove that : (1-x^(2))(d^2y)/(dx^2)+(2x-1)(d...
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If y^3-3ax^2+x^3=0, then prove that (d^2y)/(dx^2)+(2a^2x^2)/(y^5) = 0
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If y=(t a n^(-1)\ x^2) , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...
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If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0
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If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...
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If x=a(t-sint), y=a(1-cost) then find (d^2y)/(dx^2).
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If x=sint" and "y=sin mt" then prove that "sqrt(1-x^2)(d^2y)/(dx^2)-xd...
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If y=(sin^(-1)x)^2+(cos^(-1)x)^2, then prove that (1-x^2)y2-xy(1)-4=0.
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