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

The function y = cx is the solution of differential equation dddydx=yx - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

The function y = cx is the solution of differential equation `("d"y)/("d"x) = y/x`

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
Advertisements

उत्तर

This statement is True.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.8: Differential Equation and Applications - Q.3

संबंधित प्रश्‍न

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

Differential equation Function
\[x\frac{dy}{dx} = y\]
y = ax

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


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

\[\sin^4 x\frac{dy}{dx} = \cos x\]

\[\left( x^3 + x^2 + x + 1 \right)\frac{dy}{dx} = 2 x^2 + x\]

x cos2 y  dx = y cos2 x dy


\[x\sqrt{1 - y^2} dx + y\sqrt{1 - x^2} dy = 0\]

(y2 + 1) dx − (x2 + 1) dy = 0


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

\[2\left( y + 3 \right) - xy\frac{dy}{dx} = 0\], y(1) = −2

Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\]  given that y = 1, when x = 0.


Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]


Solve the following initial value problem:-

\[\left( 1 + y^2 \right) dx + \left( x - e^{- \tan^{- 1} y} \right) dx = 0, y\left( 0 \right) = 0\]


Show that all curves for which the slope at any point (x, y) on it is \[\frac{x^2 + y^2}{2xy}\]  are rectangular hyperbola.


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.


The differential equation \[x\frac{dy}{dx} - y = x^2\], has the general solution


The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.


Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.


Form the differential equation of the family of circles having centre on y-axis and radius 3 unit.


Choose the correct option from the given alternatives:

The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is


Solve the following differential equation.

`xy  dy/dx = x^2 + 2y^2`


The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.


y2 dx + (xy + x2)dy = 0


Solve: `("d"y)/("d"x) + 2/xy` = x2 


Solve the following differential equation y log y = `(log  y - x) ("d"y)/("d"x)`


The function y = ex is solution  ______ of differential equation


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


Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is ex.


The differential equation (1 + y2)x dx – (1 + x2)y dy = 0 represents a family of:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×