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Family y=Ax + A^3 of curves will corres...

Family `y=Ax + A^3 ` of curves will correspond to a differential equation of order :

A

3

B

2

C

1

D

Not defined

Text Solution

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The correct Answer is:
C
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The family y=Ax+A^(3) of curves is represents by differential equation of degree

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Represent the following family of curves by forming the corresponding differential equations (a, b are parameters) (i) x/a+y/b=1 (ii) (x^2)/(a^2)+(y^2)/(b^2)=1

Represent the following families of curves by forming the corresponding differential equations (a being parameter): (i) (x-a)^2-y^2=1 (ii) x^2+y^2=a x^3

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters): (i) x^2+(y-b)^2=1 (ii) y=a x^3

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters): (i) x^2+y^2=a^2 (ii) x^2-y^2=a^2

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters): (i) (x^2)/(a^2)-(y^2)/(b^2)=1 (ii) y=e^(a x)

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters): (i) y^2=4a x (ii) y^2=4a(x-b)

Consider the differential equation of the family of curves y^2=2a(x+sqrt(a)) , where a is a positive parameter.Statement 1: Order of the differential equation of the family of curves is 1.Statement 2: Degree of the differential equation of the family of curves is 2. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement I Differential equation corresponding to all lines, ax+by+c=0 has the order 3. Statement II Gereral solution of a differential equation of nth order contains n independent arbitaray constanis.

AAKASH INSTITUTE ENGLISH-DIFFERENTIAL EQUATIONS-Assignment (Section - A) Competition Level Questions
  1. The number of solutions of (dy)/(dx)=(y+1)/(x-1),"Then y(1)=2 is"

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  2. The differential equation y(dy)/(dx)+x=C represents

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  3. The integrating factor of differential equation (dy)/(dx)+y=(1+y)/(x)"...

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  4. The differential equation of the family of curves of x^(2)+y^(2)-2ay=0...

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  5. The general solution of (dy)/(dx)=2xe^(x^(2)-y) is

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  6. The curve in which the slope of the tangent at any point equal the rat...

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  7. The solution of equation (2y-1)dx-(2x+3)dy=0 is

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  8. Let f(x) = secx*f'(x), f(0) = 1, then f(pi/6) is equal to

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  9. The integrating factor of (1+y^(2)) dx = (tan^(-1)y-x) dy is -

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  10. The order & the degree of the differential equation whose general ...

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  11. The solution of the differential equation dy/dx=cos(x-y) is

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  12. (dy)/(dx) = (xy+y)/(xy+x), then the solution of differential equation ...

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  13. The differential equation ydy+xdx = dx represents

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  14. The integrating factor of cos^(2) x(dy)/(dx) +y = tan x is

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  15. The integrating factor of (dy)+2y = xe^(4x) is

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  16. The general solution of differential equation (dy)/(dx)=e^((x^(2))/(2)...

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  17. Family y=Ax + A^3 of curves will correspond to a differential equatio...

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  18. The solution of differential equation cos x sin y dx+sin x cos dy=0

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  19. (dy)/(dx) = (1 + y^2)/(1+x^2)

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  20. The solution of differential equation ydx + (x+xy)dy = 0 is

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