मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Choose the correct alternative: Differential equation of the function c + 4yx = 0 is

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

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

पर्याय

  • `xy + ("d"y)/("d"x)` = 0

  • `x ("d"y)/("d"x) + y` = 0

  • `("d"y)/("d"x) - 4xy` =0

  • `x ("d"y)/("d"x) + 1` = 0

MCQ
Advertisements

उत्तर

`x ("d"y)/("d"x) + y` = 0

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.8: Differential Equation and Applications - Q.1

संबंधित प्रश्‍न

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

Form the differential equation representing the family of ellipses having centre at the origin and foci on x-axis.


Show that y = AeBx is a solution of the differential equation

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

For the following differential equation verify that the accompanying function is a solution:

Differential equation Function
\[x + y\frac{dy}{dx} = 0\]
\[y = \pm \sqrt{a^2 - x^2}\]

Differential equation \[\frac{d^2 y}{d x^2} - y = 0, y \left( 0 \right) = 2, y' \left( 0 \right) = 0\] Function y = ex + e−x


\[\frac{dy}{dx} = x e^x - \frac{5}{2} + \cos^2 x\]

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

tan y \[\frac{dy}{dx}\] = sin (x + y) + sin (x − y) 

 


dy + (x + 1) (y + 1) dx = 0


\[\frac{dy}{dx} = 1 + x^2 + y^2 + x^2 y^2 , y\left( 0 \right) = 1\]

\[xy\frac{dy}{dx} = \left( x + 2 \right)\left( y + 2 \right), y\left( 1 \right) = - 1\]

\[\frac{dy}{dx} = \frac{\left( x - y \right) + 3}{2\left( x - y \right) + 5}\]

\[\frac{dy}{dx} = \sec\left( x + y \right)\]

Solve the following initial value problem:-

\[\frac{dy}{dx} + 2y = e^{- 2x} \sin x, y\left( 0 \right) = 0\]


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.


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.


A curve is such that the length of the perpendicular from the origin on the tangent at any point P of the curve is equal to the abscissa of P. Prove that the differential equation of the curve is \[y^2 - 2xy\frac{dy}{dx} - x^2 = 0\], and hence find the curve.


Which of the following is the integrating factor of (x log x) \[\frac{dy}{dx} + y\] = 2 log x?


Solve the following differential equation : \[\left( \sqrt{1 + x^2 + y^2 + x^2 y^2} \right) dx + xy \ dy = 0\].


Solve the following differential equation.

`dy/dx = x^2 y + y`


For the following differential equation find the particular solution.

`(x + 1) dy/dx − 1 = 2e^(−y)`,

when y = 0, x = 1


The integrating factor of the differential equation `dy/dx - y = x` is e−x.


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

The differential equation of y = Ae5x + Be–5x is


Solve: `("d"y)/("d"x) + 2/xy` = x2 


Solve the following differential equation

`x^2  ("d"y)/("d"x)` = x2 + xy − y2 


The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.


An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.


The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0


What distinguishes an ordinary differential equation from other types of differential equations?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×