An integrating factor of the differential equation (1 + y + x2y) dx + (x + x3) dy = 0 is
log x
x
ex
1/x
The solution of y' - y = 1 and y(0) = - 1 is given by y (x) is equal to
-1
-exp (-x)
-exp (x)
exp (x) - 2
The degree of the differential equation is
1
2
3
0
The differential equation for which y = a cosx + b sinx is a solution of
The solution of the differential equation ydx + (x + x2y) dy = 0 is.
-1/xy = c
log y = cx
1/xy + log y = c
-1/xy + log y = c
The solution of differential equation x dy - y dx = 0 represents
Rectangular hyperbola
Circle whose center is at origin
Parabola whose vertex is at origin
Straight line passing through origin
The solution of the differential equation cos x cos y dx + sin x sin y dy = 0 is
tan x = c
sin x = c cos y
sec x - sec y = c
cos x = c sin y
The differential equation representing the family of curves y2 = 2c (x + √c), where c> 0, is a parameter, is of order and degree as follows.
Order 1 and degree 1
Order 1 and degree 2
Order 2 and degree 2
Order 1 and degree 3
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
