English

In each of the following examples, verify that the given function is a solution of the corresponding differential equation. Solution D.E. y = ex dydx=y - Mathematics and Statistics

Advertisements
Advertisements

Question

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`
Sum

Solution

y = ex

Differentiating w.r.t. x, we get

`dy/dx = e^x`

∴ `dy/dx = y`

∴ Given function is a solution of the given differential equation.

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Differential Equation and Applications - Exercise 8.1 [Page 162]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.1 | Q 2.3 | Page 162

RELATED QUESTIONS

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


\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]

\[x\frac{dy}{dx} + 1 = 0 ; y \left( - 1 \right) = 0\]

xy (y + 1) dy = (x2 + 1) dx


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

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

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

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

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

Solve the following initial value problem:-

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


Solve the following initial value problem:-
\[\tan x\left( \frac{dy}{dx} \right) = 2x\tan x + x^2 - y; \tan x \neq 0\] given that y = 0 when \[x = \frac{\pi}{2}\]


Show that all curves for which the slope at any point (x, y) on it is \[\frac{x^2 + y^2}{2xy}\]  are rectangular hyperbola.


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


Solve the following differential equation.

y dx + (x - y2 ) dy = 0


`xy dy/dx  = x^2 + 2y^2`


Select and write the correct alternative from the given option for the question 

Differential equation of the function c + 4yx = 0 is


Solve the differential equation xdx + 2ydy = 0


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


Solve the differential equation

`y (dy)/(dx) + x` = 0


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×