Advertisements
Advertisements
Question
Advertisements
Solution
\[\frac{d^4 y}{d x^4} = \left[ c + \left( \frac{dy}{dx} \right)^2 \right]^\frac{3}{2} \]
Squaring both sides, we get
\[ \Rightarrow \left( \frac{d^4 y}{d x^4} \right)^2 = \left[ c + \left( \frac{dy}{dx} \right)^2 \right]^3 \]
\[ \Rightarrow \left( \frac{d^4 y}{d x^4} \right)^2 = c^3 + 3 c^2 \left( \frac{dy}{dx} \right)^2 + 3c \left( \frac{dy}{dx} \right)^4 + \left( \frac{dy}{dx} \right)^6\]
In this differential equation, the order of the highest order derivative is 4 and its power is 2. So, it is a differential equation of order 4 and degree 2.
Thus, it is a non-linear differential equation, as its degree is 2, which is greater than 1.
APPEARS IN
RELATED QUESTIONS
Verify that y = 4 sin 3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 9y = 0\]
Verify that \[y = ce^{tan^{- 1}} x\] is a solution of the differential equation \[\left( 1 + x^2 \right)\frac{d^2 y}{d x^2} + \left( 2x - 1 \right)\frac{dy}{dx} = 0\]
Solve the following differential equation:
\[y\left( 1 - x^2 \right)\frac{dy}{dx} = x\left( 1 + y^2 \right)\]
In a bank principal increases at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).
In a culture the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present.
Solve the following initial value problem:-
\[\frac{dy}{dx} + y \tan x = 2x + x^2 \tan x, y\left( 0 \right) = 1\]
The slope of the tangent at a point P (x, y) on a curve is \[\frac{- x}{y}\]. If the curve passes through the point (3, −4), find the equation of the curve.
If sin x is an integrating factor of the differential equation \[\frac{dy}{dx} + Py = Q\], then write the value of P.
The integrating factor of the differential equation (x log x)
\[\frac{dy}{dx} + y = 2 \log x\], is given by
The solution of the differential equation \[\frac{dy}{dx} - \frac{y\left( x + 1 \right)}{x} = 0\] is given by
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = ex + 1 y'' − y' = 0
The differential equation `y dy/dx + x = 0` represents family of ______.
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 |
For each of the following differential equations find the particular solution.
`y (1 + logx)dx/dy - x log x = 0`,
when x=e, y = e2.
Solve the following differential equation.
y dx + (x - y2 ) dy = 0
Solve the following differential equation.
dr + (2r)dθ= 8dθ
Choose the correct alternative.
The differential equation of y = `k_1 + k_2/x` is
The solution of `dy/dx + x^2/y^2 = 0` is ______
The integrating factor of the differential equation `dy/dx - y = x` is e−x.
y2 dx + (xy + x2)dy = 0
`xy dy/dx = x^2 + 2y^2`
Select and write the correct alternative from the given option for the question
Differential equation of the function c + 4yx = 0 is
For the differential equation, find the particular solution (x – y2x) dx – (y + x2y) dy = 0 when x = 2, y = 0
For the differential equation, find the particular solution
`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
The function y = ex is solution ______ of differential equation
