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Choose the correct alternative: General solution of y-xdydx = 0 is

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प्रश्न

Choose the correct alternative:

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

विकल्प

  • `3log x + 7/y` = c

  • `2log x + 3/y = c`

  • log x – log y = log c

  • `3log y + 2/x` = c

MCQ
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उत्तर

log x – log y = log c

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.8: Differential Equation and Applications - Q.1

संबंधित प्रश्न

\[y\frac{d^2 x}{d y^2} = y^2 + 1\]

Show that the function y = A cos x + B sin x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + y = 0\]


Verify that \[y = e^{m \cos^{- 1} x}\] satisfies the differential equation \[\left( 1 - x^2 \right)\frac{d^2 y}{d x^2} - x\frac{dy}{dx} - m^2 y = 0\]


Show that the differential equation of which \[y = 2\left( x^2 - 1 \right) + c e^{- x^2}\]  is a solution is \[\frac{dy}{dx} + 2xy = 4 x^3\]


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


\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]

\[\cos x\frac{dy}{dx} - \cos 2x = \cos 3x\]

C' (x) = 2 + 0.15 x ; C(0) = 100


xy dy = (y − 1) (x + 1) dx


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

\[\frac{dy}{dx} = e^{x + y} + e^y x^3\]

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

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

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

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

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

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


Solve the following initial value problem:-

\[\frac{dy}{dx} - 3y \cot x = \sin 2x; y = 2\text{ when }x = \frac{\pi}{2}\]


The population of a city increases at a rate proportional to the number of inhabitants present at any time t. If the population of the city was 200000 in 1990 and 250000 in 2000, what will be the population in 2010?


The differential equation satisfied by ax2 + by2 = 1 is


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

Solution D.E.
xy = log y + k y' (1 - xy) = y2

Solve the following differential equation.

`dy/dx + y` = 3


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

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


Solve the following differential equation `("d"y)/("d"x)` = x2y + y


Solve the following differential equation 

sec2 x tan y dx + sec2 y tan x dy = 0

Solution: sec2 x tan y dx + sec2 y tan x dy = 0

∴ `(sec^2x)/tanx  "d"x + square` = 0

Integrating, we get

`square + int (sec^2y)/tany  "d"y` = log c

Each of these integral is of the type

`int ("f'"(x))/("f"(x))  "d"x` = log |f(x)| + log c

∴ the general solution is

`square + log |tan y|` = log c

∴ log |tan x . tan y| = log c

`square`

This is the general solution.


Given that `"dy"/"dx" = "e"^-2x` and y = 0 when x = 5. Find the value of x when y = 3.


If `y = log_2 log_2(x)` then `(dy)/(dx)` =


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


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