हिंदी

Determine the order and degree of the following differential equations. Solution D.E. y = 1 − logx x2d2ydx2=1

Advertisements
Advertisements

प्रश्न

Determine the order and degree of the following differential equations.

Solution D.E.
y = 1 − logx `x^2(d^2y)/dx^2 = 1`
योग
Advertisements

उत्तर

y = 1 – log x

Differentiating w.r.t. x, we get

`dy/dx = -1/x`

Again, differentiating w.r.t. x, we get

`(d^2y)/dx^2 = 1/x^2`

∴ `x^2(d^2y)/dx^2 = 1`

∴  Given function is a solution of the given differential equation.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Differential Equation and Applications - Exercise 8.1 [पृष्ठ १६२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 8 Differential Equation and Applications
Exercise 8.1 | Q 2.4 | पृष्ठ १६२

संबंधित प्रश्न

\[x + \left( \frac{dy}{dx} \right) = \sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]

Differential equation \[\frac{dy}{dx} = y, y\left( 0 \right) = 1\]
Function y = ex


Differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} = 0, y \left( 0 \right) = 2, y'\left( 0 \right) = 1\]

Function y = ex + 1


\[5\frac{dy}{dx} = e^x y^4\]

\[\frac{dy}{dx} = 1 - x + y - xy\]

\[\frac{dy}{dx} = \left( \cos^2 x - \sin^2 x \right) \cos^2 y\]

y ex/y dx = (xex/y + y) dy


Solve the following initial value problem:-

\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x} , y\left( 1 \right) = 0\]


Solve the following initial value problem:-

\[\frac{dy}{dx} + 2y \tan x = \sin x; y = 0\text{ when }x = \frac{\pi}{3}\]


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?


Find the equation to the curve satisfying x (x + 1) \[\frac{dy}{dx} - y\]  = x (x + 1) and passing through (1, 0).


Find the equation of the curve which passes through the origin and has the slope x + 3y− 1 at any point (x, y) on it.


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.


Find the solution of the differential equation
\[x\sqrt{1 + y^2}dx + y\sqrt{1 + x^2}dy = 0\]


The differential equation
\[\frac{dy}{dx} + Py = Q y^n , n > 2\] can be reduced to linear form by substituting


In the following example, verify that the given function is a solution of the corresponding differential equation.

Solution D.E.
y = xn `x^2(d^2y)/dx^2 - n xx (xdy)/dx + ny =0`

For  the following differential equation find the particular solution.

`dy/ dx = (4x + y + 1),

when  y = 1, x = 0


Solve the following differential equation.

`dy /dx +(x-2 y)/ (2x- y)= 0`


The solution of `dy/ dx` = 1 is ______.


Choose the correct alternative.

The integrating factor of `dy/dx -  y = e^x `is ex, then its solution is


Select and write the correct alternative from the given option for the question 

Differential equation of the function c + 4yx = 0 is


Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0


Solve: `("d"y)/("d"x) + 2/xy` = x2 


Choose the correct alternative:

General solution of `y - x ("d"y)/("d"x)` = 0 is


Verify y = `a + b/x` is solution of `x(d^2y)/(dx^2) + 2 (dy)/(dx)` = 0

y = `a + b/x`

`(dy)/(dx) = square`

`(d^2y)/(dx^2) = square`

Consider `x(d^2y)/(dx^2) + 2(dy)/(dx)`

= `x square + 2 square`

= `square`

Hence y = `a + b/x` is solution of `square`


Solve: `("d"y)/("d"x) = cos(x + y) + sin(x + y)`. [Hint: Substitute x + y = z]


Solve the differential equation

`x + y dy/dx` = x2 + y2


Which of the following is an example of an ordinary differential equation?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×