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`x=acostheta+bsintheta`and `y=asintheta-bcostheta,`show that `y^2(d^2y)/(dx^2)-x(dy)/(dx)+y=0` |
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Answer» `y = asintheta-bcostheta` `x = acostheta+bsintheta` `=>dx/(d theta) = -asintheta+bcostheta` `=>dy/(d theta) = ` `:.dy/dx = dy/(d theta)*(d theta)/dx = (acostheta+bsintheta)/(-asintheta+bcostheta)` `=>dy/dx = x/(-y)` `=>(d^2y)/dx^2 = (-y + xdy/dx)/y^2` `=>y^2(d^2y)/dx^2-xdy/dx+y =0` |
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