Advertisements
Advertisements
Question
Advertisements
Solution
\[\left( \frac{dy}{dx} \right)^2 + \frac{1}{\left( \frac{dy}{dx} \right)} = 2\]
In this equation, the order of the highest order derivative is 1 and its highest power is 3. So, it is a differential equation of order 1 and degree 3.
APPEARS IN
RELATED QUESTIONS
Assume that a rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.
Show that the differential equation of which y = 2(x2 − 1) + \[c e^{- x^2}\] is a solution, is \[\frac{dy}{dx} + 2xy = 4 x^3\]
Show that the differential equation of which \[y = 2\left( x^2 - 1 \right) + c e^{- x^2}\] is a solution is \[\frac{dy}{dx} + 2xy = 4 x^3\]
Differential equation \[\frac{dy}{dx} = y, y\left( 0 \right) = 1\]
Function y = ex
Differential equation \[\frac{dy}{dx} + y = 2, y \left( 0 \right) = 3\] Function y = e−x + 2
x cos2 y dx = y cos2 x dy
xy dy = (y − 1) (x + 1) dx
(y + xy) dx + (x − xy2) dy = 0
Solve the following differential equation:
\[xy\frac{dy}{dx} = 1 + x + y + xy\]
Solve the following differential equation:
\[\left( 1 + y^2 \right) \tan^{- 1} xdx + 2y\left( 1 + x^2 \right)dy = 0\]
Solve the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + \left( 1 + y^2 \right) = 0\], given that y = 1, when x = 0.
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
In a bank principal increases at the rate of r% per year. Find the value of r if ₹100 double itself in 10 years (loge 2 = 0.6931).
Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
(x + y) (dx − dy) = dx + dy
Solve the following initial value problem:-
\[\frac{dy}{dx} - 3y \cot x = \sin 2x; y = 2\text{ when }x = \frac{\pi}{2}\]
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 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.
The differential equation obtained on eliminating A and B from y = A cos ωt + B sin ωt, is
The solution of the differential equation y1 y3 = y22 is
Solve the following differential equation : \[\left( \sqrt{1 + x^2 + y^2 + x^2 y^2} \right) dx + xy \ dy = 0\].
Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constant.
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
Find the particular solution of the differential equation `"dy"/"dx" = "xy"/("x"^2+"y"^2),`given that y = 1 when x = 0
Solve the following differential equation.
xdx + 2y dx = 0
Solve the following differential equation.
`xy dy/dx = x^2 + 2y^2`
Solve the following differential equation.
`(x + a) dy/dx = – y + a`
Choose the correct alternative.
The integrating factor of `dy/dx - y = e^x `is ex, then its solution is
A solution of a differential equation which can be obtained from the general solution by giving particular values to the arbitrary constants is called ___________ solution.
Select and write the correct alternative from the given option for the question
The differential equation of y = Ae5x + Be–5x is
Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0
Solve the differential equation `("d"y)/("d"x) + y` = e−x
Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0
The function y = ex is solution ______ of differential equation
The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.
