The solution of differential equation log ( dy/dx) = ax + by is
None of these
The solution of differential equation is
log ( 1 + y2 ) = tan -1 x + c
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 dy/dx + y/x = x2 is.
4xy = x4 + c
xy = x4 + c
4xy - x4 + c
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 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 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.
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 x dy/dx = y ( log y - log x + 1 ) is
Log x/y = cy
Log y/x = cy
log x/y = cx
lot y/x = cx
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