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

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. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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.

रिकाम्या जागा भरा

उत्तर

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

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Differential Equation and Applications - Miscellaneous Exercise 8 [पृष्ठ १७२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
पाठ 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 2.3 | पृष्ठ १७२

संबंधित प्रश्‍न

Assume that a rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.

 

Verify that y2 = 4a (x + a) is a solution of the differential equations
\[y\left\{ 1 - \left( \frac{dy}{dx} \right)^2 \right\} = 2x\frac{dy}{dx}\]


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

Function y = ex + 1


\[\left( x + 2 \right)\frac{dy}{dx} = x^2 + 3x + 7\]

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

\[\frac{dy}{dx} = \cos^3 x \sin^2 x + x\sqrt{2x + 1}\]

\[\frac{dy}{dx} = x e^x - \frac{5}{2} + \cos^2 x\]

C' (x) = 2 + 0.15 x ; C(0) = 100


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

tan y \[\frac{dy}{dx}\] = sin (x + y) + sin (x − y) 

 


y (1 + ex) dy = (y + 1) ex dx


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

 


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

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


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

(x2 − y2) dx − 2xy dy = 0


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

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:
\[x\frac{dy}{dx} + y = x \cos x + \sin x, y\left( \frac{\pi}{2} \right) = 1\]


Experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment. Its half-life is 1590 years. What percentage will disappear in one year?


Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y + 2 (x + 1) = 2e2x.


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.


Solve the differential equation:

`"x"("dy")/("dx")+"y"=3"x"^2-2`


Solve the following differential equation.

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


Solve the differential equation `("d"y)/("d"x) + y` = e−x 


For the differential equation, find the particular solution (x – y2x) dx – (y + x2y) dy = 0 when x = 2, y = 0


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


Choose the correct alternative:

General solution of `y - x ("d"y)/("d"x)` = 0 is


If `y = log_2 log_2(x)` then `(dy)/(dx)` =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×