Advertisements
Advertisements
प्रश्न
Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.
Advertisements
उत्तर
We have,
\[y = Cx + 5 . . . . . \left( 1 \right)\]
\[ \Rightarrow \frac{dy}{dx} = C\]
\[\text{ Substituting the value of C in }\left( 1 \right),\text{ we get }\]
\[y = \frac{dy}{dx} \times x + 5\]
\[ \Rightarrow x\frac{dy}{dx} - y + 5 = 0 \]
\[\text{ Hence, }x\frac{dy}{dx} - y + 5 = 0\text{ is the differential equation representing the family of straight lines }y = Cx + 5, \text{ where C is an arbitary constant . }\]
APPEARS IN
संबंधित प्रश्न
Prove that:
`int_0^(2a)f(x)dx = int_0^af(x)dx + int_0^af(2a - x)dx`
Verify that y = − x − 1 is a solution of the differential equation (y − x) dy − (y2 − x2) dx = 0.
x cos2 y dx = y cos2 x dy
(1 − x2) dy + xy dx = xy2 dx
tan y \[\frac{dy}{dx}\] = sin (x + y) + sin (x − y)
In a bank principal increases at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).
(x2 − y2) dx − 2xy dy = 0
\[\frac{dy}{dx} = \frac{y}{x} + \sin\left( \frac{y}{x} \right)\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + y \tan x = 2x + x^2 \tan x, y\left( 0 \right) = 1\]
Solve the following initial value problem:-
\[\frac{dy}{dx} - 3y \cot x = \sin 2x; y = 2\text{ when }x = \frac{\pi}{2}\]
A bank pays interest by continuous compounding, that is, by treating the interest rate as the instantaneous rate of change of principal. Suppose in an account interest accrues at 8% per year, compounded continuously. Calculate the percentage increase in such an account over one year.
The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.
Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y\] sin x = 1, is
The solution of the differential equation \[\frac{dy}{dx} = \frac{ax + g}{by + f}\] represents a circle when
The integrating factor of the differential equation \[x\frac{dy}{dx} - y = 2 x^2\]
The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.
Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constant.
For the following differential equation find the particular solution.
`dy/ dx = (4x + y + 1),
when y = 1, x = 0
Solve the following differential equation.
`xy dy/dx = x^2 + 2y^2`
The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.
Solve the differential equation:
dr = a r dθ − θ dr
Solve:
(x + y) dy = a2 dx
Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is ex.
Solve the differential equation
`y (dy)/(dx) + x` = 0
