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Solve the following differential equatio...

Solve the following differential equation: `(1+e^(x//y))dx+e^(x//y)(1-x/y)dy=0`

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To solve the differential equation \( (1 + e^{\frac{x}{y}})dx + e^{\frac{x}{y}}(1 - \frac{x}{y})dy = 0 \), we will follow these steps: ### Step 1: Rewrite the equation We start by rewriting the equation in the form: \[ (1 + e^{\frac{x}{y}})dx + e^{\frac{x}{y}}(1 - \frac{x}{y})dy = 0 \] This can be rearranged as: ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve the following differential equation:(dy)/(dx)=y/x+sin(y/x)

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  2. Solve the following differential equation: x ylog(x/y)dx+{y^2-x^2log(x...

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  3. Solve the following differential equation: (1+e^(x//y))dx+e^(x//y)(1-x...

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  4. Solve the following differential equation: (x^2-2x y)\ dy+(x^2-3xy+2y^...

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  5. Solve the following differential equation: x(dy)/(dx)=y-xcos^2(y/x)

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  6. Solve the following differential equation: \ x(dy)/(dx)-y=2\ sqrt(y^2-...

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

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

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

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

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

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

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  13. Solve the differential equation - (x-2y)dx+(2x+y)dy=0

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

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

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  16. Solve the following differential equation: \ x(dy)/(dx)=y-xcos^2(y/x)

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  17. Solve the following differential equation: x(dy)/(dx)-y+xsin(y/x)=0

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  18. Solve each of the following initial value problem: (x^2+y^2)dx=2x y\ d...

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  19. Solve each of the following initial value problem: x e^(y//x)-y+x(dy)/...

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  20. Solve each of the following initial value problem: (dy)/(dx)-y/x+cos e...

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