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

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

पर्याय

  • `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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पाठ 1.8: Differential Equation and Applications - Q.1

संबंधित प्रश्‍न

Show that the differential equation of which y = 2(x2 − 1) + \[c e^{- x^2}\] is a solution, is \[\frac{dy}{dx} + 2xy = 4 x^3\]


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


\[x\frac{dy}{dx} + 1 = 0 ; y \left( - 1 \right) = 0\]

\[\frac{dy}{dx} = \frac{1 - \cos 2y}{1 + \cos 2y}\]

(ey + 1) cos x dx + ey sin x dy = 0


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

dy + (x + 1) (y + 1) dx = 0


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

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

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

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

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

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

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

The rate of growth of a population is proportional to the number present. If the population of a city doubled in the past 25 years, and the present population is 100000, when will the city have a population of 500000?


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.


The rate of increase of bacteria in a culture is proportional to the number of bacteria present and it is found that the number doubles in 6 hours. Prove that the bacteria becomes 8 times at the end of 18 hours.


Find the solution of the differential equation
\[x\sqrt{1 + y^2}dx + y\sqrt{1 + x^2}dy = 0\]


y2 dx + (x2 − xy + y2) dy = 0


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`


y2 dx + (xy + x2)dy = 0


Solve the following differential equation

`x^2  ("d"y)/("d"x)` = x2 + xy − y2 


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


Verify y = `a + b/x` is solution of `x(d^2y)/(dx^2) + 2 (dy)/(dx)` = 0

y = `a + b/x`

`(dy)/(dx) = square`

`(d^2y)/(dx^2) = square`

Consider `x(d^2y)/(dx^2) + 2(dy)/(dx)`

= `x square + 2 square`

= `square`

Hence y = `a + b/x` is solution of `square`


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


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


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


The value of `dy/dx` if y = |x – 1| + |x – 4| at x = 3 is ______.


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