Advertisements
Advertisements
Question
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.
Options
y =`"e"^(x - y) = x^2 "e"^-y + "c"`
`"e"^y - "e"^x = x^3/3 + "c"`
`"e"^x + "e"^y = x^3/3 + "c"`
`"e"^x - "e"^y = x^3/3 + "c"`
Advertisements
Solution
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is `"e"^y - "e"^x = x^3/3 + "c"`.
Explanation:
The given differential equation is `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y`
⇒ `("d"y)/("d"x) = "e"^x . "e"^-y + x^2 . "e"^-y`
⇒ `("d"y)/("d"x) = "e"^-y ("e"^x + x^2)`
⇒ `("d"y)/"e"^-y = ("e"^x + x^2)"d"x`
⇒ `"e"^y . "d"y = ("e"^x + x^2)"d"x`
Integrating both sides, we have
`int "e"^x "d"y = int ("e"^x + x^2) "d"x`
⇒ `"e"^y = "e"^x + x^3/3 + "c"`
⇒ `"e"^y - "e"^x = x^3/3 + "c"`
APPEARS IN
RELATED QUESTIONS
Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0.
Find the differential equation representing the curve y = cx + c2.
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
If y = etan x+ (log x)tan x then find dy/dx
Solve the differential equation `cos^2 x dy/dx` + y = tan x
The general solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x}\] is
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that
Solve the differential equation (x2 − yx2) dy + (y2 + x2y2) dx = 0, given that y = 1, when x = 1.
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
\[\frac{dy}{dx} - y \tan x = e^x \sec x\]
`y sec^2 x + (y + 7) tan x(dy)/(dx)=0`
\[y^2 + \left( x + \frac{1}{y} \right)\frac{dy}{dx} = 0\]
`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`
Find the general solution of the differential equation \[\frac{dy}{dx} = \frac{x + 1}{2 - y}, y \neq 2\]
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x-coordinate and the product of the x-coordinate and y-coordinate of that point.
Find the differential equation of all non-horizontal lines in a plane.
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
Find the general solution of (1 + tany)(dx – dy) + 2xdy = 0.
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
Solution of differential equation xdy – ydx = 0 represents : ______.
The general solution of ex cosy dx – ex siny dy = 0 is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The solution of `x ("d"y)/("d"x) + y` = ex is ______.
The differential equation for which y = acosx + bsinx is a solution, is ______.
General solution of `("d"y)/("d"x) + ytanx = secx` is ______.
General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.
The value of c in the particular solution given that y(0) = 0 and k = 0.049 is ______.
Find a particular solution, satisfying the condition `(dy)/(dx) = y tan x ; y = 1` when `x = 0`
Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.
If the solution curve of the differential equation `(dy)/(dx) = (x + y - 2)/(x - y)` passes through the point (2, 1) and (k + 1, 2), k > 0, then ______.
