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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`

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

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

\[\sqrt[3]{\frac{d^2 y}{d x^2}} = \sqrt{\frac{dy}{dx}}\]

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

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

\[\sin\left( \frac{dy}{dx} \right) = k ; y\left( 0 \right) = 1\]

\[\frac{dy}{dx} = \frac{1 + y^2}{y^3}\]

(1 + x2) dy = xy dx


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

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

In a bank principal increases at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).


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

Solve the following initial value problem:-

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


If the marginal cost of manufacturing a certain item is given by C' (x) = \[\frac{dC}{dx}\] = 2 + 0.15 x. Find the total cost function C (x), given that C (0) = 100.

 

Experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment. Its half-life is 1590 years. What percentage will disappear in one year?


Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.


What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?


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

For each of the following differential equations find the particular solution.

(x − y2 x) dx − (y + x2 y) dy = 0, when x = 2, y = 0


Solve the following differential equation

`yx ("d"y)/("d"x)` = x2 + 2y2 


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


Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.


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