Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
In this differential equation, the order of the highest order derivative is 2 and its power is 1. So, it is a differential equation of order 2 and degree 1.
It is a linear differential equation.
APPEARS IN
संबंधित प्रश्न
Differential equation \[\frac{d^2 y}{d x^2} - y = 0, y \left( 0 \right) = 2, y' \left( 0 \right) = 0\] Function y = ex + e−x
(1 − x2) dy + xy dx = xy2 dx
y ex/y dx = (xex/y + y) dy
(x + 2y) dx − (2x − y) dy = 0
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{xy}{x^2 + y^2}\] given that y = 1 when x = 0.
The population of a city increases at a rate proportional to the number of inhabitants present at any time t. If the population of the city was 200000 in 1990 and 250000 in 2000, what will be the population in 2010?
Find the equation of the curve such that the portion of the x-axis cut off between the origin and the tangent at a point is twice the abscissa and which passes through the point (1, 2).
Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C2.
The differential equation
\[\frac{dy}{dx} + Py = Q y^n , n > 2\] can be reduced to linear form by substituting
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.
Solve the differential equation:
`"x"("dy")/("dx")+"y"=3"x"^2-2`
Find the particular solution of the differential equation `"dy"/"dx" = "xy"/("x"^2+"y"^2),`given that y = 1 when x = 0
Form the differential equation from the relation x2 + 4y2 = 4b2
Solve the following differential equation.
`x^2 dy/dx = x^2 +xy - y^2`
Solve the following differential equation.
`(x + y) dy/dx = 1`
The integrating factor of the differential equation `dy/dx - y = x` is e−x.
State whether the following is True or False:
The degree of a differential equation is the power of the highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any.
y2 dx + (xy + x2)dy = 0
Solve the differential equation `("d"y)/("d"x) + y` = e−x
The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.
lf the straight lines `ax + by + p` = 0 and `x cos alpha + y sin alpha = p` are inclined at an angle π/4 and concurrent with the straight line `x sin alpha - y cos alpha` = 0, then the value of `a^2 + b^2` is
A man is moving away from a tower 41.6 m high at a rate of 2 m/s. If the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower, is
Which of the following defines a differential equation?
What distinguishes an ordinary differential equation from other types of differential equations?
