Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 + xy = 0\]
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 non-linear differential equation, as the differential coefficient \[\frac{dy}{dx}\] has exponent 2, which is greater than 1.
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 y2 = 4a (x + a) is a solution of the differential equations
\[y\left\{ 1 - \left( \frac{dy}{dx} \right)^2 \right\} = 2x\frac{dy}{dx}\]
Verify that \[y = e^{m \cos^{- 1} x}\] satisfies the differential equation \[\left( 1 - x^2 \right)\frac{d^2 y}{d x^2} - x\frac{dy}{dx} - m^2 y = 0\]
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[x\frac{dy}{dx} + y = y^2\]
|
\[y = \frac{a}{x + a}\]
|
(ey + 1) cos x dx + ey sin x dy = 0
\[\frac{dy}{dx} = \frac{y}{x} + \sin\left( \frac{y}{x} \right)\]
Find the equation of the curve which passes through the point (1, 2) and the distance between the foot of the ordinate of the point of contact and the point of intersection of the tangent with x-axis is twice the abscissa of the point of contact.
Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.
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 solution of the differential equation y1 y3 = y22 is
Show that y = ae2x + be−x is a solution of the differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} - 2y = 0\]
y2 dx + (x2 − xy + y2) dy = 0
Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constant.
Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.
Choose the correct option from the given alternatives:
The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is
In the following example, verify that the given function is a solution of the corresponding differential equation.
| Solution | D.E. |
| xy = log y + k | y' (1 - xy) = y2 |
Solve the following differential equation.
`xy dy/dx = x^2 + 2y^2`
x2y dx – (x3 + y3) dy = 0
Solve the differential equation `("d"y)/("d"x) + y` = e−x
Solve: `("d"y)/("d"x) + 2/xy` = x2
For the differential equation, find the particular solution
`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0
Choose the correct alternative:
Differential equation of the function c + 4yx = 0 is
Solve the following differential equation
`y log y ("d"x)/("d"y) + x` = log y
Given that `"dy"/"dx"` = yex and x = 0, y = e. Find the value of y when x = 1.
Solve the differential equation
`y (dy)/(dx) + x` = 0
