A differential equation whose equation is y = cx + x2, where c is a constant, is _________.
dy/dx = y + x2
dy/dx + y = x2
x.dy/dx - y = x2
x.dy/dx + y/x = x2
The solution of dy/dx = (y/x)1/3 is
x2/3 + y2/3 =C
x1/3 + y1/3 =C
y2/3 - x2/3 =C
y1/3 - x1/3 =C
Integrating factor of dy/dx +y/x = x3 - 3 is
x
logx
-x
ex
The order of the differential equation of all conics whose center lie at the origin is given by
2
3
4
None of these
The general solution of excosydx - ex sinydy = 0 is
ex(siny + cosy)=C
exsiny = C
excosy = C
ex = Csiny
The order of the differential equation of all circles of radius 'a' is
1
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 particular solution of dy/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 equation of the curve whose slope at any point different from origin is y+ y/x is
y = cxex ,c ≠0
y = xex
xy = ex
y +xex = c
Solution of x2 + y2dy/dx = 4 is
x2 + y2 =12x +C
x2 + y2 = 3x +C
x3+ y3 = 3x +C
x3+ y3 = 12x +C
