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Solve the following differential equatio...

Solve the following differential equation: `y sqrt(1+x^2)+xsqrt(1+y^(2 ))(dy)/(dx)=0`

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To solve the differential equation \[ y \sqrt{1+x^2} + x \sqrt{1+y^2} \frac{dy}{dx} = 0, \] we can follow these steps: ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. (e^y+1)cosx dx+e^ysinx dy=0

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

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  3. Solve the following differential equation: y sqrt(1+x^2)+xsqrt(1+y^(2 ...

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  4. The solution of the equation (dy)/(dx)=(x(2logx+1))/(siny+ycosy) is

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  5. Solve the following differential equation: tanydx+sec^2ytanx dy=0

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  6. Solve the following differential equation: tany(dy)/(dx)=sin(x+y)+sin(...

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  7. Solve the following differential equation:(dy)/(dx)+(cosxsiny)/(cosy)=...

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  8. Solve the following differential equation: y (1+e^x)dy=(y+1)e^x dx

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

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  10. Solve the following differential equation: dy+(x+1)(y+1)dx=0

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  11. Solve the following differential equation: (x-1)(dy)/(dx)=2x^3y

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  12. Solve the following differential equation: (dy)/(dx)=(cos^2x-sin^2x)co...

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  13. Solve the following differential equation: cosec x log y(dy)/(dx)+\ x...

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

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  15. Solve the differential equation y e^(x/y)dx=(x e^(x/y)+y^2)dy(y!=0)

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  16. Solve the following differential equation: (1+y^2)tan^(-1)dx+2y(1+x^2)...

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  17. Solve the following initial value problem: (dy)/(dx)=y \ tan2x ,\ y(0)...

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  18. Solve the following initial value problem: x y(dy)/(dx)=y+2,\ y(2)=0

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  19. Solve the following initial value problem: (d r)/(dt)=\ -r t ,\ r(0) =...

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  20. Solve the following initial value problem: (dy)/(dx)=ytanx ,\ y(0)=1

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