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

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

Advertisements
Advertisements

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
Advertisements

उत्तर

log x – log y = log c

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.8: Differential Equation and Applications - Q.1

संबंधित प्रश्‍न

\[\frac{d^3 x}{d t^3} + \frac{d^2 x}{d t^2} + \left( \frac{dx}{dt} \right)^2 = e^t\]

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

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

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


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

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


\[\frac{dy}{dx} = x \log x\]

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

dy + (x + 1) (y + 1) dx = 0


Solve the following differential equation: 
(xy2 + 2x) dx + (x2 y + 2y) dy = 0


\[\frac{dy}{dx} = \frac{\left( x - y \right) + 3}{2\left( x - y \right) + 5}\]

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

2xy dx + (x2 + 2y2) dy = 0


Solve the following initial value problem:-

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


Solve the following initial value problem:-

\[dy = \cos x\left( 2 - y\text{ cosec }x \right)dx\]


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?


Find the equation of the curve passing through the point \[\left( 1, \frac{\pi}{4} \right)\]  and tangent at any point of which makes an angle tan−1  \[\left( \frac{y}{x} - \cos^2 \frac{y}{x} \right)\] with x-axis.


The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.


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

Solution D.E.
y = ex  `dy/ dx= y`

Solve the following differential equation.

(x2 − y2 ) dx + 2xy dy = 0


Solve the following differential equation.

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


Solve the following differential equation.

dr + (2r)dθ= 8dθ


The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.


Choose the correct alternative.

Bacteria increases at the rate proportional to the number present. If the original number M doubles in 3 hours, then the number of bacteria will be 4M in


Solve the differential equation:

dr = a r dθ − θ dr


Given that `"dy"/"dx"` = yex and x = 0, y = e. Find the value of y when x = 1.


An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.


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×