Advertisements
Advertisements
प्रश्न
Solve the following differential equation `("d"y)/("d"x)` = x2y + y
उत्तर
`("d"y)/("d"x)` = x2y + y
= (x2 + 1)y
∴ `1/y "d"y` = (x2 + 1) dx
Integrating on both sides, we get
`int 1/y "d"y = int(x^2 + 1) "d"x`
∴ log |y| = `x^3/3 + x + c`
APPEARS IN
संबंधित प्रश्न
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.
(ey + 1) cos x dx + ey sin x dy = 0
In a culture the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present.
3x2 dy = (3xy + y2) dx
The rate of growth of a population is proportional to the number present. If the population of a city doubled in the past 25 years, and the present population is 100000, when will the city have a population of 500000?
Find the equation of the curve which passes through the origin and has the slope x + 3y− 1 at any point (x, y) on it.
The slope of the tangent at each point of a curve is equal to the sum of the coordinates of the point. Find the curve that passes through the origin.
Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.
Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C2.
Solve the differential equation:
dr = a r dθ − θ dr
Solve the differential equation `("d"y)/("d"x) + y` = e−x
Solve the following differential equation y2dx + (xy + x2) dy = 0
State whether the following statement is True or False:
The integrating factor of the differential equation `("d"y)/("d"x) - y` = x is e–x
An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.
Solve the differential equation
`x + y dy/dx` = x2 + y2
