Advertisements
Advertisements
Question
Solution
In this differential equation, the order of the highest order derivative is 3 and its power is 1. So, it is a differential equation of order 3 and degree 1.
It is a non-linear differential equation because the differential coefficient \[\frac{dx}{dt}\] has exponent 2, which is greater than 1.
APPEARS IN
RELATED QUESTIONS
Show that the function y = A cos 2x − B sin 2x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 4y = 0\].
Verify that \[y = ce^{tan^{- 1}} x\] is a solution of the differential equation \[\left( 1 + x^2 \right)\frac{d^2 y}{d x^2} + \left( 2x - 1 \right)\frac{dy}{dx} = 0\]
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[y = \left( \frac{dy}{dx} \right)^2\]
|
\[y = \frac{1}{4} \left( x \pm a \right)^2\]
|
(ey + 1) cos x dx + ey sin x dy = 0
(1 − x2) dy + xy dx = xy2 dx
\[x^2 \frac{dy}{dx} = x^2 + xy + y^2 \]
(y2 − 2xy) dx = (x2 − 2xy) dy
Solve the following initial value problem:-
\[\frac{dy}{dx} + 2y = e^{- 2x} \sin x, y\left( 0 \right) = 0\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + y\cot x = 2\cos x, y\left( \frac{\pi}{2} \right) = 0\]
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.
Find the equation to the curve satisfying x (x + 1) \[\frac{dy}{dx} - y\] = x (x + 1) and passing through (1, 0).
At every point on a curve the slope is the sum of the abscissa and the product of the ordinate and the abscissa, and the curve passes through (0, 1). Find the equation of the curve.
Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.
Which of the following differential equations has y = C1 ex + C2 e−x as the general solution?
y2 dx + (x2 − xy + y2) dy = 0
Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.
Solve the following differential equation.
`(dθ)/dt = − k (θ − θ_0)`
Solve the following differential equation.
`dy/dx + 2xy = x`
Solve the following differential equation.
dr + (2r)dθ= 8dθ
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.
`xy dy/dx = x^2 + 2y^2`
Solve the differential equation xdx + 2ydy = 0
Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0
Solve the following differential equation
`yx ("d"y)/("d"x)` = x2 + 2y2
Solve the following differential equation y log y = `(log y - x) ("d"y)/("d"x)`
A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution
