Advertisements
Advertisements
प्रश्न
The function y = ex is solution ______ of differential equation
Advertisements
उत्तर
`("d"y)/("d"x) = y`
APPEARS IN
संबंधित प्रश्न
If 1, `omega` and `omega^2` are the cube roots of unity, prove `(a + b omega + c omega^2)/(c + s omega + b omega^2) = omega^2`
Show that the function y = A cos x + B sin x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + y = 0\]
(y + xy) dx + (x − xy2) dy = 0
Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]
The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of the balloon after `t` seconds.
x2 dy + y (x + y) dx = 0
Find the equation of the curve passing through the point \[\left( 1, \frac{\pi}{4} \right)\] and tangent at any point of which makes an angle tan−1 \[\left( \frac{y}{x} - \cos^2 \frac{y}{x} \right)\] with x-axis.
Find the equation to the curve satisfying x (x + 1) \[\frac{dy}{dx} - y\] = x (x + 1) and passing through (1, 0).
Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.
Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.
The differential equation of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = C\] is
Which of the following is the integrating factor of (x log x) \[\frac{dy}{dx} + y\] = 2 log x?
Which of the following differential equations has y = C1 ex + C2 e−x as the general solution?
For the following differential equation find the particular solution.
`(x + 1) dy/dx − 1 = 2e^(−y)`,
when y = 0, x = 1
Solve the following differential equation.
`x^2 dy/dx = x^2 +xy - y^2`
Solve the differential equation:
`e^(dy/dx) = x`
y dx – x dy + log x dx = 0
Solve the following differential equation `("d"y)/("d"x)` = x2y + y
The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0
