English

Form the differential equation of y = (c1 + c2)ex

Advertisements
Advertisements

Question

Form the differential equation of y = (c1 + c2)ex 

Sum
Advertisements

Solution

y = (c1 + c2)ex 

= Aex,     ...(i)

Where A = (c1 + c2)

Here, A is an arbitrary constant.

Differentiating (i) w.r.t. x, we get

`("d"y)/("d"x)` = Aex

∴ `("d"y)/("dx)` = y     ......[From (i)]

shaalaa.com
  Is there an error in this question or solution?
Chapter 2.6: Differential Equations - Attempt the following questions I

RELATED QUESTIONS

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y2 = (x + c)3


Find the differential equation of the ellipse whose major axis is twice its minor axis.


Form the differential equation of all parabolas whose axis is the X-axis.


In the following example verify that the given expression is a solution of the corresponding differential equation:

xy = log y +c; `"dy"/"dx" = "y"^2/(1 - "xy")`


In the following example verify that the given expression is a solution of the corresponding differential equation:

y = xm; `"x"^2 ("d"^2"y")/"dx"^2 - "mx" "dy"/"dx" + "my" = 0`


In the following example verify that the given expression is a solution of the corresponding differential equation:

y = `"a" + "b"/"x"; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" = 0`


Solve the following differential equation:

cos x . cos y dy − sin x . sin y dx = 0


For the following differential equation find the particular solution satisfying the given condition:

3ex tan y dx + (1 + ex) sec2 y dy = 0, when x = 0, y = π.


Reduce the following differential equation to the variable separable form and hence solve:

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


Choose the correct option from the given alternatives:

The solution of `"dy"/"dx" = ("y" + sqrt("x"^2 - "y"^2))/"x"` is


Choose the correct option from the given alternatives:

The solution of `"dy"/"dx" + "y" = cos "x" - sin "x"`


The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.


Choose the correct option from the given alternatives:

The solution of the differential equation `"dy"/"dx" = sec "x" - "y" tan "x"`


The particular solution of `dy/dx = xe^(y - x)`, when x = y = 0 is ______.


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

`"y" = "e"^"ax" sin "bx"; ("d"^2"y")/"dx"^2 - 2"a" "dy"/"dx" + ("a"^2 + "b"^2)"y" = 0`


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

`"y" = 3 "cos" (log "x") + 4 sin (log "x"); "x"^2 ("d"^2"y")/"dx"^2 + "x" "dy"/"dx" + "y" = 0`


Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = `"Ae"^(3"x" + 1) + "Be"^(- 3"x" + 1)`


Solve the following differential equation:

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


Solve the following differential equation:

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


Solve the following differential equation:

y log y = (log y2 - x) `"dy"/"dx"`


Find the particular solution of the following differential equation:

(x + y)dy + (x - y)dx = 0; when x = 1 = y


Find the particular solution of the following differential equation:

`2e ^(x/y) dx + (y - 2xe^(x/y)) dy = 0," When" y (0) = 1`


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

Solution of the equation `x  ("d"y)/("d"x)` = y log y is


Form the differential equation of family of standard circle


Find the differential equation by eliminating arbitrary constants from the relation y = (c1 + c2x)ex 


Find the differential equation of the family of all non-horizontal lines in a plane 


Form the differential equation of all straight lines touching the circle x2 + y2 = r2


Find the differential equation of the family of circles passing through the origin and having their centres on the x-axis


Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to the x-axis


Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be –8x, where A and B are arbitrary constants


Find the differential equation of the curve represented by xy = aex + be–x + x2


The general solution of the differential equation of all circles having centre at A(- 1, 2) is ______.


The elimination of the arbitrary constant m from the equation y = emx gives the differential equation ______.


The differential equation representing the family of parabolas having vertex at origin and axis along positive direction of X-axis is ______.


The differential equation whose solution is (x – h)2 + (y – k)2 = a2 is (where a is a constant) ______.


If y = (tan–1 x)2 then `(x^2 + 1)^2 (d^2y)/(dx^2) + 2x(x^2 + 1) (dy)/(dx)` = ______.


The differential equation of all parabolas whose axis is Y-axis, is ______.


The differential equation of the family of circles touching Y-axis at the origin is ______.


The differential equation of all circles passing through the origin and having their centres on the X-axis is ______.


If 2x = `y^(1/m) + y^(-1/m)`, then show that `(x^2 - 1) (dy/dx)^2` = m2y2


Solve the differential equation

ex tan y dx + (1 + ex) sec2 y dy = 0


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×