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 order of the differential equation is
1
2
3
4
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 degree of the differential equation is
5
The solution of dy/dx = ex+y + x2 ey; y(0) = 0 is
The particular solution of edy/dx = x + 1 given that x = 0, y = 3 is
y = x log (x + 1) - x + 3
y = (x + 1) log (x + 1) - x + 3
y = (x + 1) log (x + 1) - x + 2
y = (x + 1) log (x + 1) - x + 1
The order of the differential equation dy/dx = sinx is
0
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 order and degree of the diff:equation are
2,2
2,1
1, 2
2, 3
tan-1x + tan-1y = c is the general solution of the differential equation
(1 + x2)dy + (1 + y2)dx = 0