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Find the differential equation of the fa...

Find the differential equation of the family of curves `y= Ae^(x)+Be^(-x)`, where A and B are constants.

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The correct Answer is:
`(d^(2)y)/(dx^2)-y=0`
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ARIHANT PUBLICATION-DIFFERENTIAL EQUATION-CHAPTER PRACTICE (VERY SHORT ANSWER TYPE QUESTIONS)
  1. Write the differential equation representing the family of curves y= m...

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  2. Find the differential equation of the family of concentric circles hav...

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  3. Find the differential equation of the family of curves y= Ae^(x)+Be^(-...

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  4. Form the differential equation by aliminating A and B in Ax^(2)+By^(2)...

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  5. Find the differential equation corresponding to curve y= a cos (x+b), ...

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  6. Solve the following differential equations : (dy)/(dx)= sqrt(1-y^2),...

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  7. Solve the following differential equations : (dy)/(dx)+y=1, y ne 1.

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  8. Solve the following differential equations : (dy)/(dx)-(y(x+1))/(x)=...

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  9. Solve the following differential equations : (dy)/(dx)=e^(x+y)+x^(2)...

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  10. Write the solution of differential equation (e^(x)+e^(-x))dy= (e^(x)-e...

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  11. If (dy)/(dx)=ye^(x)" and "x=0, y= e, then find the value of y, when x=...

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  12. Solve 2(y+3)-xy(dy)/(dx)=0, given that y(1)= -2.

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  13. Solve the differential equation (dy)/(dx)= y sin 2x, given that y(0)= ...

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  14. Solve the initial value problem dy= e^(2x+y)dx, y(0)= 0.

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  15. Find the equation of a curve passing through the point (-2,3), given t...

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  16. Show that the given differential equation is homogeneous ans solve it ...

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  17. Find the integrating factor of the differential equation x(dy)/(dx)-y=...

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  18. Find the integrating factor of the differential equation (1-y^2)(dx)/(...

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  19. Write the integrating factor of (dy)/(dx)-(1)/((1+x))y=(1+x)e^(x).

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  20. Write the integrating factor of the differential equation sqrt(x) (dy)...

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