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Prove that x^2-y^2=c(x^2+y^2)^2is the ...

Prove that `x^2-y^2=c(x^2+y^2)^2`is the general solution of differential equation `(x^3-2xy^2)dx=(y^3-3x^2y)dy`, where c is a parameter.

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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-Revision Exercise
  1. Verify that x^(2)=2y^(2)log y is a solution of the differential equati...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Solve each of the following initial value problems: (dy)/(dx)+(2x)/...

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  19. If ye^(y) dx = (y^(3) + 2xe^(y))dy, y(0) = 1, then the value of x when...

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  20. Find the particular solution of the differential equation (1+e^(2x))dy...

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