" n."(dy)/(dx)+(1+x^(2))/(x)=0

If y=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)++(x^(n))/(n!), show that (dy)/(dx)-y+(x^(n))/(n!)=0

(y-x(dy)/(dx))=3(1-x^(2)(dy)/(dx))

If y=1+x+(x^(2))/(2!)+(x^(3))/(3!)+....+(x^(n))/(n!) , then show that (dy)/(dx)+(x^(n))/(n!)=y

If y=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)+ . . .+(x^(n))/(n!) , prove that (dy)/(dx)+(x^(n))/(n!)=y

If "(dy)/(dx)+(2y)/(x)=0 ,y(1)=1" then y(2)=(1)/(n') "(n in N)" .value of "n" is

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

If y=x^(n){a cos(log x)+b sin(log x)}, prove that x^(2)(d^(2)y)/(dx^(2))+(1-2n)(dy)/(dx)+(1+n^(2))y=0

((dy)/(dx))+((1)/(x))y=x^(n)

If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)-y+(x^n)/(n !)=0.