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For each of the problems, given below, v...

For each of the problems, given below, verify that the given function ( implicit or explicit) is a solution of the corresponding differential equation :
`y=x sin 3x " " : " " (d^(2)y)/(dx^(2))+9y-6 cos 3x = 0`

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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-Revision Exercise
  1. For each of the exercises given below, verify that the given function...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Solve each of the following initial value problem: (y^4-2x^3y)dx+(x^4-...

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  20. Solve each of the following initial value problem: x(x^2+3y^2)dx+y(y^2...

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