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If `y=acos(logx)+sin(logx),`prove that`(x^2d^2)/(dx^2)+ x(dy)/(dx)+y=0` |
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Answer» `y = acos(logx)+bsin(logx)` Let `logx = t =>1/xdx = dt=>dt/dx = 1/x` Then, `y = acost+bsint` `=>dy/dt = -asint+bcost` `:.dy/dx = dy/dt*dt/dx = (-asint+bcost)1/x` `=>xdy/dx = bcost-asint` Differentiating w.r.t. `x`, `=>x(d^2y)/dx^2+dy/dx = (-bsint-acost)dt/dx` `=>x(d^2y)/dx^2+dy/dx = -y/x` `=>x^2(d^2y)/dx^2+xdy/dx+y = 0` |
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