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

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प्रश्न

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is True.

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अध्याय 1.8: Differential Equation and Applications - Q.3

संबंधित प्रश्न

\[\frac{d^3 x}{d t^3} + \frac{d^2 x}{d t^2} + \left( \frac{dx}{dt} \right)^2 = e^t\]

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

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


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

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

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


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

 


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

\[\frac{dy}{dx} + 1 = e^{x + y}\]

y ex/y dx = (xex/y + y) dy


Find the curve for which the intercept cut-off by a tangent on x-axis is equal to four times the ordinate of the point of contact.

 

Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C2.


Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y\] sin x = 1, is


y2 dx + (x2 − xy + y2) dy = 0


Form the differential equation from the relation x2 + 4y2 = 4b2


For  the following differential equation find the particular solution.

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

when  y = 1, x = 0


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 ______.


Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`


Given that `"dy"/"dx"` = yex and x = 0, y = e. Find the value of y when x = 1.


Solution of `x("d"y)/("d"x) = y + x tan  y/x` is `sin(y/x)` = cx


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