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For each of the exercises given below, ...

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.(i) `y=a e^x+b e^(-x)+x^2` : `x(d^2y)/(dx^2)+2y(dy)/(dx)-x y+x^2-2=0`(ii) `y=e^x(acosx+bsin

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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-Revision Exercise
  1. For each of the differential equations given below, indicate its orde...

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  2. Find the order and degree (if defined) of the equation: (d^4y)/(dx^4)...

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  3. For each of the exercises given below, verify that the given function...

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  4. The differential equation for y=e^(x)(acosx+bsinx) is

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  5. For each of the problems, given below, verify that the given function ...

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  6. Verify that x^(2)=2y^(2)log y is a solution of the differential equati...

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  7. Obtain the differential equation of the family of circles passing thro...

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  8. Prove that x^2-y^2=c(x^2+y^2)^2is the general solution of differenti...

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  9. Find the general solution of each of the following differential equat...

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  10. Solve : (dy)/(dx)=(x e^(x)log x +e^(x))/(x cos y).

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  11. Solve : (1+x^(2)+y^(2)+x^(2)y^(2))dx+xy dy=0, given that y=0 when x=1.

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  12. Solve x((dy)/(dx))=y(logy-logx+1)

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  13. The slope of the tangent at a point P(x, y) on a curve is (- (y+3)/(x+...

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  14. Find the equation of the curve passing through the point (0,pi/4) w...

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  15. Find the equation of a curve passing through the point (1, 1), given t...

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  16. The decay rate of radium at any time t is proportional to its mass ...

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  17. Solve : (dy)/(dx)= (2x+3y-4)^(2).

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  18. Solve: (dy)/(dx)+y=e^x

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  19. Solve the following differential equation: (x^2-1)(dy)/(dx)+2(x+2)y=2\...

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  20. Solve: (dy)/(dx) = (y ( x + 2y))/(x ( 2x + y)) ,y(1) = 2

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