The Order and degree of differential equation are
1 and 1/2
2 and 1
1 and 1
1 and 2
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 + 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 ( 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
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 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 is
sin -1 y + sin -1 x = c
sin -1 y - sin -1 x = c
sin -1 x + 2 sin -1 y = c
2 sin -1 y - sin -1 x = c
None of these
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.
