On putting y = vx, the homogeneous DE x2dy + y ( x + y) dx = 0 becomes :
xdv + ( 2v + V2 ) dx = 0
vdx + (2x + x2) dv =0
V2dx - ( x + x2 ) dv = 0
vdv + ( 2x + x2 ) dx = 0
The solution of differential equation x2 dy/dx = x2 + xy + y2 is
tan -1 ( y/x ) = log x + c
tan-1 (x/y) = log x + c
tan -1 ( x/y ) = log y + c
None of these
The solution of differential equation is.
(1 + y2 ) (1 + x 2 ) = cx2
(1 - y2 ) (1 + x 2 ) = cx2
(1 + y2 ) (1 - x 2 ) = cx2
(1 - y2 ) (1 - x 2 ) = cx2
The solution of differential equation dy/dx + y tan x = sec x is
sin x
( sin x ) -1
e sin x
( cos x ) -1
The solution of differential equation is
y sin y = x2 log x + x2/2 + c
y cos y = x2 ( log x + 1 ) + c
y cos y = x2 log x + x2/2 + c
y sin y = x2 log x + c
The solution of differential equation (x2 - y2 ) dy/dx = xy is .
log ( 1 + y2 ) = tan -1 x + c
The solution of differential equation dy/dx + 2y = sinx is
y = 5 ( 2 sinx - cos x ) + c e 2x
y = ( 2 sinx - cos x ) + ce -x
y = ( 2 cos - sin x ) + ce - 2x
y = 1/5 ( 2 sinx - cos x ) + ce - 2 x.
The solution of differential equation ( x2 - yx2 ) dy + ( y2 + x2y2) dx = 0 is
1/x + y + log y = c
1/y+ y + 1/y 2 = c
1/y + 1/x + log y - x = c
The solution of differential equation ( 1 - y ) x dy/dx + ( 1 + x ) y = 0 is
log xy + x + y = c
log xy + x -y =c
log xy - x - y = c
