Advertisements
Advertisements
प्रश्न
उत्तर
In this differential equation, the order of the highest order derivative is 2 and its power is 3. So, it is a differential equation of order 2 and degree 3.
It is a non-linear differential equation, as its degree is more than 1.
APPEARS IN
संबंधित प्रश्न
If 1, `omega` and `omega^2` are the cube roots of unity, prove `(a + b omega + c omega^2)/(c + s omega + b omega^2) = omega^2`
Solve the equation for x: `sin^(-1) 5/x + sin^(-1) 12/x = pi/2, x != 0`
Form the differential equation representing the family of ellipses having centre at the origin and foci on x-axis.
Verify that y = − x − 1 is a solution of the differential equation (y − x) dy − (y2 − x2) dx = 0.
(sin x + cos x) dy + (cos x − sin x) dx = 0
Solve the following differential equation:
\[xy\frac{dy}{dx} = 1 + x + y + xy\]
Solve the following differential equation:
\[y e^\frac{x}{y} dx = \left( x e^\frac{x}{y} + y^2 \right)dy, y \neq 0\]
Solve the following differential equation:
\[\left( 1 + y^2 \right) \tan^{- 1} xdx + 2y\left( 1 + x^2 \right)dy = 0\]
Solve the following initial value problem:-
\[x\frac{dy}{dx} - y = \log x, y\left( 1 \right) = 0\]
A population grows at the rate of 5% per year. How long does it take for the population to double?
Find the equation of the curve passing through the point (0, 1) if the slope of the tangent to the curve at each of its point is equal to the sum of the abscissa and the product of the abscissa and the ordinate of the point.
Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y\] sin x = 1, is
The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.
The price of six different commodities for years 2009 and year 2011 are as follows:
Commodities | A | B | C | D | E | F |
Price in 2009 (₹) |
35 | 80 | 25 | 30 | 80 | x |
Price in 2011 (₹) | 50 | y | 45 | 70 | 120 | 105 |
The Index number for the year 2011 taking 2009 as the base year for the above data was calculated to be 125. Find the values of x andy if the total price in 2009 is ₹ 360.
For the following differential equation find the particular solution.
`(x + 1) dy/dx − 1 = 2e^(−y)`,
when y = 0, x = 1
Solve the following differential equation.
`(x + y) dy/dx = 1`
Choose the correct alternative.
The differential equation of y = `k_1 + k_2/x` is
The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.
Solve:
(x + y) dy = a2 dx
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 = cx is the solution of differential equation `("d"y)/("d"x) = y/x`
Solve the differential equation `"dy"/"dx" + 2xy` = y