Advertisements
Advertisements
Question
Find the general solution of the following differential equation:
`(dy)/(dx) = e^(x-y) + x^2e^-y`
Advertisements
Solution
Given differential equation is `(dy)/(dx) = e^(x-y) + x^2e^-y`
⇒ `(dy)/(dx) = e^-y(e^x + x^2)`
⇒ `(dy)/e^-y = dx(e^x + x^2)`
⇒ `e^ydy = e^xdx + x^2dx`
On integrating both sides, we get
`e^y = e^x + x^3/3 + c`
APPEARS IN
RELATED QUESTIONS
Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`
Determine the order and degree (if defined) of the differential equation:
y' + 5y = 0
Determine the order and degree (if defined) of the differential equation:
( y′′′) + (y″)3 + (y′)4 + y5 = 0
Determine the order and degree (if defined) of the differential equation:
y′′′ + 2y″ + y′ = 0
Write the order of the differential equation whose solution is y = a cos x + b sin x + c e−x.
Write the order and degree of the differential equation
\[\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^\frac{1}{4} + x^\frac{1}{5} = 0\]
The order of the differential equation whose general solution is given by y = c1 cos (2x + c2) − (c3 + c4) ax + c5 + c6 sin (x − c7) is
Determine the order and degree (if defined) of the following differential equation:-
y" + 2y' + sin y = 0
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = x2 + 2x + C y' − 2x − 2 = 0
Determine the order and degree of the following differential equation:
`(dy)/(dx) = (2sin x + 3)/(dy/dx)`
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`
Determine the order and degree of the following differential equations.
`sqrt(1+1/(dy/dx)^2) = (dy/dx)^(3/2)`
Choose the correct alternative:
The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` are respectively
The order and degree of the differential equation `("d"^2"y")/"dx"^2 + (("d"^3"y")/"dx"^3) + x^(1/5) = 0` are respectively.
The order and degree of the differential equation `[1 + ("dy"/"dx")^2]^2 = ("d"^2y)/("d"x^2)` respectively, are ______.
Order of the differential equation representing the family of ellipses having centre at origin and foci on x-axis is two.
The order and degree of the differential equation `(("d"^3y)/("d"x^3))^2 - 3 ("d"^2y)/("d"x^2) + 2(("d"y)/("d"x))^4` = y4 are ______.
If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.
The differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.
The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is ______.
The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))` respectively are ______.
The order and degree of the differential equation `sqrt(dy/dx) - 4 dy/dx - 7x` = 0 are ______.
The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.
Assertion: Degree of the differential equation: `a(dy/dx)^2 + bdx/dy = c`, is 3
Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as polynomial) then highest exponent of the highest order derivative is called the degree of the differential equation.
Which of the following is correct?
