If `y=e^x(sinx+cosx)"p r o v et h a t"(d^2y)/(dx^2)-2(dy)/(dx)+2y=0.`

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If y=e^x(sin x+cosx) prove that (d^2y)/(dx^2)-2 (dy)/(dx)+2y=0 .

If y=e^x(sinx+cosx) prove that (d^2y)/(dx^2)-2(dy)/(dx)+2y=0 .

If y = e^x (sinx + cosx) , prove that (d^2y)/(dx^2)- 2(dy)/(dx) + 2y = 0

If x=sint ,y=sinp t ,"p r o v et h a t" (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

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If y="sin"(sinx),"p r o v et h a t" (d^2y)/(dx^2)+tanx(dy)/(dx)+ycos^2x=0.

If y=e^(x)sinx , then prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0 ,

If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

If y=e^(x)sinx, prove that (D^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0 .

If y="log"(1+cosx),"p r o v et h a t"(d^3y)/(dx^3)+(d^2y)/(dx^2)dot(dy)/(dx)=0.