The solution of 2(y + 3) - xy dy/dx = 0 with y = -2, when x = 1 is
(y + 3) = x2
x2 (y + 3) = 1
x4(y + 3) = 1
x2 (y + 3)3 = ey+2
The solution of dy/dx = ex+y + x2 ey; y(0) = 0 is
The diff: equation corresponding to y2 - 2ay + x2 = a2 by eliminating a is
(dy/dx)2 (x2 - 2y2) - 4 (dy/dx)xy - x2 = 0
(dy/dx)2 (y2 - 2x2) - 4.dy/dx . xy - x2 = 0
(dy/dx)2 . y2 - 4. dy/dx . xy - x2 = 0
(dy/dx)2(x2 - 2y2) - 4. dy/dx - x2 = 0
tan-1x + tan-1y = c is the general solution of the differential equation
(1 + x2)dy + (1 + y2)dx = 0
The order and degree of the diff:equation are
2,2
2,1
1, 2
2, 3
An integrating factor of the diff: equation (1 + y + x2y) dx + (x + x3) dy = 0 is
log x
x
ex
1/x
Solution of (x2 + 3xy + y2) dx - x2dy = 0 is
None of these
The differential equation corresponding to y = kx is
y = x. dy/dx
y = k. dy/dx
dy/dx = k. dy/dx
y = kx + c
The general solution of the equation dy/dx = x5 + x2 - 2/x is
0 = x2/6 + x3/3 = 2 logx + c
y = x6/6 + x3/3 - 2 logx + c
y = x5/5 + x4/x - 2 logx + c
y = x6/6 + x3/x - logx + c
The degree of the differential equation is
1
2
3
0
