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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
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उत्तर

This statement is True.

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अध्याय 1.8: Differential Equation and Applications - Q.3

संबंधित प्रश्न

Show that y = e−x + ax + b is solution of the differential equation\[e^x \frac{d^2 y}{d x^2} = 1\]

 


\[\frac{dy}{dx} = x^2 + x - \frac{1}{x}, x \neq 0\]

\[\frac{1}{x}\frac{dy}{dx} = \tan^{- 1} x, x \neq 0\]

C' (x) = 2 + 0.15 x ; C(0) = 100


\[\cos x \cos y\frac{dy}{dx} = - \sin x \sin y\]

\[\frac{dy}{dx} + \frac{\cos x \sin y}{\cos y} = 0\]

Solve the following differential equation:
\[xy\frac{dy}{dx} = 1 + x + y + xy\]

 


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

 


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

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

\[\frac{dy}{dx} = 1 + x + y^2 + x y^2\] when y = 0, x = 0

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

Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]


(x + y) (dx − dy) = dx + dy


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

\[x^2 \frac{dy}{dx} = x^2 - 2 y^2 + xy\]

\[\frac{dy}{dx} = \frac{x}{2y + x}\]

Solve the following initial value problem:
\[x\frac{dy}{dx} + y = x \cos x + \sin x, y\left( \frac{\pi}{2} \right) = 1\]


Find the equation of the curve which passes through the point (2, 2) and satisfies the differential equation
\[y - x\frac{dy}{dx} = y^2 + \frac{dy}{dx}\]


The normal to a given curve at each point (x, y) on the curve passes through the point (3, 0). If the curve contains the point (3, 4), find its equation.


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


In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

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


Solve the differential equation:

`"x"("dy")/("dx")+"y"=3"x"^2-2`


Determine the order and degree of the following differential equations.

Solution D.E
y = aex + be−x `(d^2y)/dx^2= 1`

Solve the following differential equation.

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


Solve the following differential equation.

y dx + (x - y2 ) dy = 0


Solve the differential equation:

`e^(dy/dx) = x`


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


Choose the correct alternative:

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


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


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