Advertisements
Advertisements
प्रश्न
Solve the following differential equation.
`dy/dx + y` = 3
उत्तर
`dy/dx + y` = 3
The given equation is of the form
`dy/dx + py = Q`
where, P = 1 and Q = 3
∴ I.F. = `e int^(pdx) = e int^ (1dx) = e^x`
∴ Solution of the given equation is
`y(I.F.) = int Q(I.F.) dx + c`
∴ `ye^x = int 3e^x dx + c`
∴ yex = 3ex + c
संबंधित प्रश्न
Verify that y = \[\frac{a}{x} + b\] is a solution of the differential equation
\[\frac{d^2 y}{d x^2} + \frac{2}{x}\left( \frac{dy}{dx} \right) = 0\]
Differential equation \[x\frac{dy}{dx} = 1, y\left( 1 \right) = 0\]
Function y = log x
xy dy = (y − 1) (x + 1) dx
Solve the following initial value problem:-
\[x\frac{dy}{dx} - y = \log x, y\left( 1 \right) = 0\]
Solve the following initial value problem:-
\[\tan x\left( \frac{dy}{dx} \right) = 2x\tan x + x^2 - y; \tan x \neq 0\] given that y = 0 when \[x = \frac{\pi}{2}\]
The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time t.
Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.
The differential equation \[x\frac{dy}{dx} - y = x^2\], has the general solution
The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.
Verify that the function y = e−3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + \frac{dy}{dx} - 6y = 0.\]
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
Choose the correct option from the given alternatives:
The differential equation `"y" "dy"/"dx" + "x" = 0` represents family of
Form the differential equation from the relation x2 + 4y2 = 4b2
Solve the following differential equation.
`y^3 - dy/dx = x dy/dx`
Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`
Solve: `("d"y)/("d"x) + 2/xy` = x2
Choose the correct alternative:
General solution of `y - x ("d"y)/("d"x)` = 0 is
Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is ex.
There are n students in a school. If r % among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?
