मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Select and write the correct alternative from the given option for the question The solution of dydx = 1 is

Advertisements
Advertisements

प्रश्न

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

The solution of `("d"y)/("d"x)` = 1 is

पर्याय

  • x + y = c

  • xy = c

  • x2 + y2 = c

  • y – x = c

MCQ
Advertisements

उत्तर

y – x = c

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.6: Differential Equations - MCQ

संबंधित प्रश्‍न

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

x3 + y3 = 4ax


Form the differential equation of family of lines having intercepts a and b on the co-ordinate ares respectively.


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


Find the differential equation of all circles having radius 9 and centre at point (h, k).


Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.


Solve the following differential equation:

`"dy"/"dx" = (1 + "y")^2/(1 + "x")^2`


Solve the following differential equation:

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


Solve the following differential equation:

`(cos^2y)/x dy + (cos^2x)/y dx` = 0


Solve the following differential equation:

`2"e"^("x + 2y") "dx" - 3"dy" = 0`


Solve the following differential equation:

(x2 + y2)dx - 2xy dy = 0


Choose the correct option from the given alternatives:

x2 + y2 = a2 is a solution of


Choose the correct option from the given alternatives:

The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is


Choose the correct option from the given alternatives:

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


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

`"x"^2 + "y"^2 = "r"^2; "x" "dy"/"dx" + "r" sqrt(1 + ("dy"/"dx")^2) = "y"`


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`


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

`"x"^2 = "2y"^2 log "y",  "x"^2 + "y"^2 = "xy" "dx"/"dy"`


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

y = a sin (x + b)


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:

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:

y(1 + log x) = (log xx) `"dy"/"dx"`, when y(e) = e2


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


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

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


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

The solutiion of `("d"y)/("d"x) + x^2/y^2` = 0 is


Find the differential equation of family of lines making equal intercepts on coordinate axes


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


Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0


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


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 equations of the family of all the ellipses having foci on the y-axis and centre at the origin


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


Choose the correct alternative:

The slope at any point of a curve y = f(x) is given by `("d"y)/("d"x) - 3x^2` and it passes through (-1, 1). Then the equation of the curve is


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 ______.


Form the differential equation of all lines which makes intercept 3 on x-axis.


For the curve C: (x2 + y2 – 3) + (x2 – y2 – 1)5 = 0, the value of 3y' – y3 y", at the point (α, α), α < 0, on C, is equal to ______.


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


The differential equation for a2y = log x + b, is ______.


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


Form the differential equation whose general solution is y = a cos 2x + b sin 2x.


A particle is moving along the X-axis. Its acceleration at time t is proportional to its velocity at that time. Find the differential equation of the motion of the particle.


The differential equation whose solution represents the family \[x^{2}y=4e^{x}+c\], where c is an arbitrary constant, is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×