Let `y(x)` be a solution of the differential equation `(1+e^x)y^(prime)+y e^x=1.` If `y(0)=2`, then which of the following statements is (are) true? (a)`y(-4)=0` (b)`y(-2)=0` (c)`y(x)` has a critical point in the interval `(-1,0)` (d)`y(x)` has no critical point in the interval`(-1,0)`

Solution of the differential equation y(a x y+e^x)dx-e^x dy=0 where y(0)=1 is

The solution to the differential equation ylogy+x y^(prime)=0, where y(1)=e , is

Verify that y=-x-1 is a solution of the differential equation (y-x)dy-(y^2-x^2)dx=0.

Let y(x) be a solution of the differential equation (1+e^x)y^(prime)+y e^x=1. If y(0)=2 , then which of the following statements is (are) true? (a) ( b ) (c) y(( d ) (e)-4( f ))=0( g ) (h) (b) ( i ) (j) y(( k ) (l)-2( m ))=0( n ) (o) (c) ( d ) (e) y(( f ) x (g))( h ) (i) has a critical point in the interval ( j ) (k)(( l ) (m)-1,0( n ))( o ) (p) (q) ( r ) (s) y(( t ) x (u))( v ) (w) has no critical point in the interval ( x ) (y)(( z ) (aa)-1,0( b b ))( c c ) (dd)

The general solution of the differential equation y(x^(2)y+e^(x))dx-(e^x)dy=0 , is

If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then

Let y=f(x) is a solution of differential equation e^(y)((dy)/(dx)-1)=e^(x) and f(0)=0 then f(1) is equal to

The solution of the differential equation x(dy)/(dx) + 2y = x^2 (X ne 0) with y(1) =1, is :

Find the particular solution of the differential equation: (1+e^2x)dy+(1+y^2)e^xdx=0 , given that y(0)=1

Find a particular solution of the differential equation: (x+y)dy+(x-y)dx=0; y=1\ w h e n\ x=1