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Verify that the function `y=x sin x` is a solution of the differential equation of ` x dy/dx=y+x sqrt(x^2-y^2)`

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CHETANA PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE
  1. Verify that the function y=e^(-3x) is a solution of the differential e...

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  2. Verify that xy=ae^x+be^(-x)+x^2 is a solution of the differential equa...

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  3. Verify that the function y=x sin x is a solution of the differential e...

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  4. Solve the following differential equations. (e^y+1)cos x dx+e^y sin x ...

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  5. Solve the following differential equations.y^2-dy/dx=x^2 dy/dx

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  6. Solve the following differential equations. dy/dx=(1+y^2)/(4+x^2)

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  7. Solve the following differential equations.(4)dy/dx=3^(x+y).Also,find ...

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  8. Solve the following differential equations. (1-x)dy-(1+y)dx=0.Also,fin...

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  9. Solve the following differential equations. (x-y^2x)dx-(y-x^2y)dy=0.A...

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  10. Solve the following differential equations. (1-x^2)(1-y)dx=xy(1+y)dy.

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  11. Solve the following differential equations.dy/dx=y((e^(3x)-e^(-3x))/(e...

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  12. Solve the following differential equation. y-x dy/dx=alpha (y^2+ dy/dx...

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  13. Solve the following differential equations. y(2 log y+1)dy=(sin x+cos ...

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  14. Solve the following differential equations.dy/dx=x^2y+y

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  15. Solve the following differential equations.dy/dx=sin (x+y)+cos(x+y)

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  16. Solve the following differential equations.dy/dx=(4x+3y-1)^2

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  17. Solve the following differential equations. cos^2(x-y) dy/dx=1

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  18. Solve the following differential equations.(x-y)(1- dy/dx)=e^x

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

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  20. Solve the following differential equations.(x dy/dx-y)sin (y/x)=x^2 e^...

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