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

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

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PRADEEP PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE
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  2. Show that the function y=(A+Bx)e^(3x) is a solution of the equation (d...

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

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  4. Show that function y=be^x+ce^(2x) is a solution of the differential eq...

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  5. Show that the diffential equation of which y=2(x^2-1)+Ce^(-x^2) is a s...

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  6. Solve the following differential equations (dy)/( dx) = x^5 + x^2 - ...

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  7. Solve the following differential equations (dy)/( dx) = x^2 + sin 3...

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

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  9. Solve the following differential equations (dy)/( dx) = ( x+1)/( 2-y...

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  10. Solve the following differential equations: dx=(x^2+2x+2)dy

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  11. Solve the following differential equations: (x^2+1)(dy)/(dx)=1

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

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  13. Solve the following differential equations: (x+2)(dy)/(dx)=4x^2y

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  14. Solve the following differential equations: (dy)/(dx)+2x=3^(3x)

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  15. Solve the following differential equations: (e^x+e^(-x))(dy)/(dx)=e^x-...

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  16. Solve the following differential equations: sec^2xtanydx+sec^2ytanxdy=...

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  17. Solve the following differential equations: (tan^2x+2tanx+5)(dy)/(dx)=...

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  18. Solve the following differential equations: x(e^(2y)-1)dy+(x^2-1)e^ydx...

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  19. Solve the following differential equations: cosxcosy(dy)/(dx)=-sinxsin...

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  20. Solve the following differential equations: (dy)/(dx)=(e^x+1)y

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