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Solve each of the following initial valu...

Solve each of the following initial value problem: `(x-siny)dy+(tany)dx=0,\ y(0)=0`

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The given diff. equation can be written as
`` `frac{d x}{d y}+(cot y) x=cos y`
`` This is linear differential equation.
`` ` { I.F. }=e^{int cot y d y}=e^{log sin y}=sin y`
`` ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve: y dx + ( x - y^3) dy = 0

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  2. Solve [(e^(-2sqrt(x)))/(sqrt(x))-y/(sqrt(x))](dx)/(dy)=1(x!=0)

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  3. Solve each of the following initial value problem: (x-siny)dy+(tan...

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  4. Solve each of the following initial value problem: (1+y^2)dx=(tan^...

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  5. Solve the following differential equation: (dy)/(dx)+2y=e^(3x)

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  6. Solve the following differential equation : (dy)/(dx)+2y=6e^x

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  7. Solve the following differential equation: x(dy)/(dx)+y=xlogx

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  8. Solve the following differential equation: (dy)/(dx)+y/x=x^3

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  9. Solve the following differential equation: (dy)/(dx)+y=cosx

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  10. Solve the following differential equations: (dy)/(dx)=ytanx-2sinx

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  11. Solve the following differential equation: x\ dy=(2y+2x^4+x^2)dx

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  12. Solve the following differential equation: y^2(dx)/(dy)+x-1/y=0

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  13. Solve the following differential equations: (dy)/(dx)=ytanx-2sinx

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  14. Solve the differential equation sinx(dy)/(dx)+ycosx=2sin^2xcosx

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  15. Solve the following differential equation: x(dy)/(dx)+2y=xcosx

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  16. Solve the following differential equation: 4(dy)/(dx)+8y=5\ e^(-3x)

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

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  18. Solve the following differential equation: (dy)/(dx)+2y=4x

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

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  20. Solve the following differential equation: (dy)/(dx)+y=sinx

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