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
None of these
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 dy/dx + y tan x = sec x is
sin x
( sin x ) -1
e sin x
( cos x ) -1
The solution of differential equation (x2 - y2 ) dy/dx = xy is .
The solution of differential equation ( x + y ) ( dx - dy ) = ( dx + dy ) is
x + y = ke x + y
x - y = ke x - y
x + y = Ce x - y
x - y = ke x + y
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
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
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 integrating factor of the differential equation ( 1 + y2 ) dx - ( tan -1 y - x ) dy = 0 is
tan - 1 y
e tan -1 y
1/ 1 + y2
1/ x ( a + y2 )
The solution of differential equation x dy/dx = y + x tan y/x is
sin x/y = cx
sin y/x = cx
sin x/y = cy