Advertisements
Advertisements
प्रश्न
Find the general solution of the following differential equation:
`(dy)/(dx) = e^(x-y) + x^2e^-y`
Advertisements
उत्तर
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
संबंधित प्रश्न
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′′′ + 2y″ + y′ = 0
Determine the order and degree (if defined) of the differential equation:
y″ + (y′)2 + 2y = 0
(y'')2 + (y')3 + sin y = 0
Write the degree of the differential equation \[\left( \frac{dy}{dx} \right)^4 + 3x\frac{d^2 y}{d x^2} = 0\]
Write the degree of the differential equation x \[\left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + x^3 = 0\]
Write the degree of the differential equation \[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log\left( \frac{d^2 y}{d x^2} \right)\]
The order of the differential equation \[2 x^2 \frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + y = 0\], is
Determine the order and degree (if defined) of the following differential equation:-
\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = x sin x `xy'=y+xsqrt(x^2-y^2)`
Determine the order and degree of the following differential equation:
(y''')2 + 3y'' + 3xy' + 5y = 0
Determine the order and degree of the following differential equation:
`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`
Determine the order and degree of the following differential equations.
`((d^2y)/(dx^2))^2 + ((dy)/(dx))^2 =a^x `
Fill in the blank:
The power of the highest ordered derivative when all the derivatives are made free from negative and / or fractional indices if any is called __________ of the differential equation.
Find the order and degree of the following differential equation:
`[ (d^3y)/dx^3 + x]^(3/2) = (d^2y)/dx^2`
State whether the following statement is True or False:
Order and degree of differential equation are always positive integers.
The order and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.
If m and n are the order and degree of the differential equation `((d^3y)/(dx^3))^6+5((d^3y)/(dx^3))^4/((d^4y)/(dx^4))+(d^4y)/(dx^4)=x^3-1,` then ______.
The order of the differential equation of all circles of given radius a is ______.
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 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 ______.
Degree of the differential equation `sinx + cos(dy/dx)` = y2 is ______.
If `(a + bx)e^(y/x)` = x then prove that `x(d^2y)/(dx^2) = (a/(a + bx))^2`.
Find the order and degree of the differential equation
`sqrt(1 + 1/(dy/dx)^2) = ((d^2y)/(dx^2))^(3/2)`
