Advertisements
Advertisements
प्रश्न
Solve the following differential equation:
`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`
Advertisements
उत्तर
`("d"y)/("d"x) "e"^(x + y) + x^3, ("e"^y)`
= ey[ex + x3]
`("d"y)/"e"^y` = dx(ex + x3)
The equation can be written as
`("d"y)/"e"^y` = (ex + x3)dx
Taking integration on both sides, we get
`int "e"^y "d"y = int ("e"^x + x^3) "d"x`
`"e"^y/(-1) = "e"^x + x^4/4 + "C"`
Where – C = C
Which is also constant
∴ `"e"^x + "e"^-y + x^4/4` = – C = C
∴ `"e"^x + "e"^-y + x^4/4` = C
APPEARS IN
संबंधित प्रश्न
Solve the following differential equation:
x cos y dy = ex(x log x + 1) dx
Solve the following differential equation:
`("d"y)/("d"x) = tan^2(x + y)`
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Solve the following differential equation:
`x ("d"y)/("d"x) = y - xcos^2(y/x)`
Choose the correct alternative:
If sin x is the integrating factor of the linear differential equation `("d"y)/("d"x) + "P"y = "Q"`, then P is
Choose the correct alternative:
The number of arbitrary constants in the particular solution of a differential equation of third order is
Solve: `("d"y)/("d"x) = "ae"^y`
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Solve: (1 – x) dy – (1 + y) dx = 0
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Solve the following:
`("d"y)/("d"x) + y/x = x'e"^x`
Choose the correct alternative:
The differential equation of x2 + y2 = a2
Choose the correct alternative:
Which of the following is the homogeneous differential equation?
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (f(y/x))/(f"'"(y/x))` is
Form the differential equation having for its general solution y = ax2 + bx
Solve (D2 – 3D + 2)y = e4x given y = 0 when x = 0 and x = 1
Solve `("d"y)/("d"x) = xy + x + y + 1`
