English

Solve the following differential equation. xdx + 2y dx = 0 - Mathematics and Statistics

Advertisements
Advertisements

Question

Solve the following differential equation.

xdx + 2y dx = 0

Sum

Solution

xdx + 2y dy = 0

Integrating on both sides, we get

`int x  dx +2 int y  dy = 0`

∴ `x^2/2 + (2y^2)/2 = c_1`

∴ x2 + 2y2 = c      ...[2c1 = c]

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Differential Equation and Applications - Exercise 8.4 [Page 167]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.4 | Q 1.1 | Page 167

RELATED QUESTIONS

Form the differential equation representing the family of ellipses having centre at the origin and foci on x-axis.


Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.


Verify that \[y = ce^{tan^{- 1}} x\]  is a solution of the differential equation \[\left( 1 + x^2 \right)\frac{d^2 y}{d x^2} + \left( 2x - 1 \right)\frac{dy}{dx} = 0\]


Differential equation \[\frac{dy}{dx} + y = 2, y \left( 0 \right) = 3\] Function y = e−x + 2


\[\frac{dy}{dx} = e^{x + y} + e^y x^3\]

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

\[2x\frac{dy}{dx} = 5y, y\left( 1 \right) = 1\]

x2 dy + y (x + y) dx = 0


(x2 − y2) dx − 2xy dy = 0


The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given the number triples in 5 hrs, find how many bacteria will be present after 10 hours. Also find the time necessary for the number of bacteria to be 10 times the number of initial present.


The rate of increase of bacteria in a culture is proportional to the number of bacteria present and it is found that the number doubles in 6 hours. Prove that the bacteria becomes 8 times at the end of 18 hours.


The integrating factor of the differential equation \[x\frac{dy}{dx} - y = 2 x^2\]


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


Choose the correct option from the given alternatives:

The differential equation `"y" "dy"/"dx" + "x" = 0` represents family of


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`

Form the differential equation from the relation x2 + 4y2 = 4b2


Solve the following differential equation.

`xy  dy/dx = x^2 + 2y^2`


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


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 `("d"y)/("d"x)` = x2y + y


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×