" (iii) "(dy)/(dx)+2y=e^(-2x)sin x,y(0)=0

Solve each of the following initial value problem: (dy)/(dx)+2y=e^(-2x)sin x,y(1)=0

For each of the following initial value problems verify that the accompanying functions is a solution. (i) x(dy)/(dx)=1, y(1)=0 => y=logx (ii) (dy)/(dx)=y , y(0)=1 => y=e^x (iii) (d^2y)/(dx^2)+y=0, y(0)=0, y^(prime)(0)=1 => y=sinx (iv) (d^2y)/(dx^2)-(dy)/(dx)=0, y(0)=2, y^(prime)(0)=1 => y=e^x+1 (v) (dy)/(dx)+y=2, y(0)=3 => y=e^(-x)+2

(dy)/(dx) + 2y = e ^(-2x) sinx , given that y=0 when x = 0

If (dy)/(dx)= y sin 2x, y(0)=1 , then solution is

e ^ (y) (dy) / (dx) + x ^ (3) cos x ^ (2) = 0

Express the following differential equations in the form (dx)/(dy) = F((x)/(y)) (i) (1+e^((x)/(y)))dx + e^((x)/(y))(1-(x)/(y))dy = 0 (ii) xdy - ydx + y e^(-(2x)/(y)) dy = 0

The solution of (dy)/(dx)=e^(x)(sin^(2)x+sin2x)/(y(2log y+1)) is

If y = sin (log _(e) x) then (x ^(2) (d ^(2) y)/(dx ^(2)) +x (dy )/(dx)=

If y= e^(tan x) then show that, (cos^(2)x) (d^(2)y)/(dx^(2))- (1+ sin 2x) (dy)/(dx)=0