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RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
- If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .
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- If y=2sinx+3cosx , show that (d^2y)/(dx^2)+y=0 .
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- If y=(logx)/x , show that (d^2y)/(dx^2)=(2logx-3)/(x^3) .
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- If x=asectheta , y=btantheta , prove that (d^2y)/(dx^2)=-(b^4)/(a^2\ y...
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- If x=a(costheta+thetasintheta) , y=a(sintheta-thetacostheta) , prove t...
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- If y=e^xcosx , prove that (d^2y)/(dx^2)=2\ e^xcos(x+pi/2) .
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- If x=acostheta , y=bsintheta , show that (d^2y)/(dx^2)=-(b^4)/(a^2y^3)...
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- If x=a(1-cos^3theta) , y=a\ s in^3theta , prove that (d^2y)/(dx^2)=(32...
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- If x=a(theta+sintheta) , y=a(1+costheta) , prove that (d^2y)/(dx^2)=-a...
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- If x=a(theta-sintheta) , y=a(1+costheta) find (d^2y)/(dx^2)
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- If x=a(1-costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=-1...
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- If x=a(1+costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=(-...
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- If x=costheta , y=sin^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx))...
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- If y=sin(sinx) , prove that (d^2y)/(dx^2)+tanxdot(dy)/(dx)+y\ cos^2x=0...
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- If x=sint ,y=sinp t ,"p r o v et h a t" (1-x^2)(d^2y)/(dx^2)-x(dy)/...
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- If y=(sin^(-1)x)^2 , prove that (1-x^2)y2-x y1-2=0 .
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- If y=e^tan^((-1)x) , prove that (1+x^2)y2+(2x-1)y1=0 .
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- If y=3cos(logx)+4sin(logx),\ prove that x^2y2+x\ y1+y=0 .
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- If y=e^(2x)(a x+b) , show that y2-4\ y1+4\ y=0 .
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- If x=sin(1/alogy) , show that (1-x^2)y2-x\ y1-a^2\ y=0 .
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