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

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

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

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 y = AeBx is a solution of the differential equation

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

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


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

x cos2 y  dx = y cos2 x dy


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

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

dy + (x + 1) (y + 1) dx = 0


Solve the following differential equation:
\[y e^\frac{x}{y} dx = \left( x e^\frac{x}{y} + y^2 \right)dy, y \neq 0\]

 


\[2\left( y + 3 \right) - xy\frac{dy}{dx} = 0\], y(1) = −2

Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]


Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{xy}{x^2 + y^2}\] given that y = 1 when x = 0.

 


Solve the following initial value problem:-

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


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?


A bank pays interest by continuous compounding, that is, by treating the interest rate as the instantaneous rate of change of principal. Suppose in an account interest accrues at 8% per year, compounded continuously. Calculate the percentage increase in such an account over one year.


The slope of the tangent at each point of a curve is equal to the sum of the coordinates of the point. Find the curve that passes through the origin.


Define a differential equation.


The integrating factor of the differential equation (x log x)
\[\frac{dy}{dx} + y = 2 \log x\], is given by


Which of the following is the integrating factor of (x log x) \[\frac{dy}{dx} + y\] = 2 log x?


Choose the correct option from the given alternatives:

The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is


Determine the order and degree of the following differential equations.

Solution D.E.
ax2 + by2 = 5 `xy(d^2y)/dx^2+ x(dy/dx)^2 = y dy/dx`

Solve the following differential equation.

xdx + 2y dx = 0


Solve the following differential equation.

`xy  dy/dx = x^2 + 2y^2`


Solve the following differential equation.

y dx + (x - y2 ) dy = 0


A solution of a differential equation which can be obtained from the general solution by giving particular values to the arbitrary constants is called ___________ solution.


Solve the following differential equation y2dx + (xy + x2) dy = 0


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


There are n students in a school. If r % among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?


A man is moving away from a tower 41.6 m high at a rate of 2 m/s. If the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower, is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×