हिंदी

Choose the correct alternative: Solution of the equation ddxdydx = y log y is - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

Solution of the equation `x("d"y)/("d"x)` = y log y is

विकल्प

  • y = aex 

  • y = be2x 

  • y = be–2x 

  • y = eax

MCQ
Advertisements

उत्तर

y = eax

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

संबंधित प्रश्न

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

Verify that y = \[\frac{a}{x} + b\] is a solution of the differential equation
\[\frac{d^2 y}{d x^2} + \frac{2}{x}\left( \frac{dy}{dx} \right) = 0\]


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

Function y = log x


Differential equation \[\frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + 2y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 3\] Function y = ex + e2x


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

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

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

x cos2 y  dx = y cos2 x dy


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

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

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

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

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

Find the particular solution of edy/dx = x + 1, given that y = 3, when x = 0.


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).


Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.


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

Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]


Solve the following initial value problem:-

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


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.

 

Show that all curves for which the slope at any point (x, y) on it is \[\frac{x^2 + y^2}{2xy}\]  are rectangular hyperbola.


The equation of the curve whose slope is given by \[\frac{dy}{dx} = \frac{2y}{x}; x > 0, y > 0\] and which passes through the point (1, 1) is


Find the differential equation whose general solution is

x3 + y3 = 35ax.


Solve the following differential equation.

`dy/dx + y = e ^-x`


Solve the following differential equation.

y dx + (x - y2 ) dy = 0


Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0


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


A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution


Solve: `("d"y)/("d"x) = cos(x + y) + sin(x + y)`. [Hint: Substitute x + y = z]


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×