If ` y = Ae^(6x) +Be^(-x)` prove that `(d^(2)y)/(dx^(2)) - 5 (dy)/(dx) - 6y = 0 `

If y= 3e^(2x)+2e^(3x) , prove that (d^(2)y)/(dx^(2))-5(dy)/(dx)+6y=0 .

If y= Ae^(mx) +Be^(nx) , show that (d^(2)y)/(dx^(2))-(m+n)(dy)/(dx)+mny=0 .

If y=(cos^(-1)x)^(2) prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-2=0

If y = ( cos^(-1) x)^2 , prove that (1-x^2) (d^2 y)/(dx^2) - x(dy)/(dx) - 2=0 . Hence find y_2 when x=0 .

If y= 5 cos x-3 sin x , prove that (d^(2)y)/(dx^(2))+y=0 .

If y=(cos^(-1) x)^(2) prove that (1-x^(2)) (d^(2)y)/(dx^(2)) -x(dy)/(dx) -2=0 . Hence find y_(2) when x=0.

(a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

If y= (cos^(-1) x)^2 , prove that (1-x^2) (d^2y)/(dx^2) - x(dy)/(dx) -2 =0 , Hence find y_2 when x=0 .

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2

If y=(cos^(-1)x)^(2) prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-2=0 . Hence find y_(2) when x=0