English

The solution of dydx+x2y2=0 is

Advertisements
Advertisements

Question

The solution of `dy/dx + x^2/y^2 = 0` is ______

Options

  • x3 + y3 = 7

  • x2 + y2 = c

  • x3 + y3 = c

  • x + y = c

MCQ
Fill in the Blanks
Advertisements

Solution

The solution of `dy/dx + x^2/y^2 = 0` is x3 + y3 = c

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Differential Equation and Applications - Miscellaneous Exercise 8 [Page 171]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 1.06 | Page 171

RELATED QUESTIONS

Show that y = ax3 + bx2 + c is a solution of the differential equation \[\frac{d^3 y}{d x^3} = 6a\].

 


Show that y = ex (A cos x + B sin x) is the solution of the differential equation \[\frac{d^2 y}{d x^2} - 2\frac{dy}{dx} + 2y = 0\]


Verify that \[y = e^{m \cos^{- 1} x}\] satisfies the differential equation \[\left( 1 - x^2 \right)\frac{d^2 y}{d x^2} - x\frac{dy}{dx} - m^2 y = 0\]


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


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

Solve the following differential equation:
\[y\left( 1 - x^2 \right)\frac{dy}{dx} = x\left( 1 + y^2 \right)\]

 


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

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

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

Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\]  given that y = 1, when x = 0.


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


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

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


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

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.


Which of the following differential equations has y = C1 ex + C2 e−x as the general solution?


Find the coordinates of the centre, foci and equation of directrix of the hyperbola x2 – 3y2 – 4x = 8.


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

Solution D.E.
y = xn `x^2(d^2y)/dx^2 - n xx (xdy)/dx + ny =0`

Solve the following differential equation.

`dy/dx + y` = 3


Solve the following differential equation.

`(x + y) dy/dx = 1`


Choose the correct alternative.

The differential equation of y = `k_1 + k_2/x` is


Solve

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


 `dy/dx = log x`


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)`


For the differential equation, find the particular solution

`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0


Solve the following differential equation

`y log y ("d"x)/("d"y) + x` = log y


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


`d/(dx)(tan^-1  (sqrt(1 + x^2) - 1)/x)` is equal to:


The differential equation (1 + y2)x dx – (1 + x2)y dy = 0 represents a family of:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×