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Solve the following differential equatio...

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

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To solve the differential equation \((x-1) \frac{dy}{dx} = 2x^3 y\), we will follow these steps: ### Step 1: Rearrange the equation We start by rewriting the equation to separate the variables \(y\) and \(x\): \[ (x-1) dy = 2x^3 y dx \] ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve the following differential equation: x y(dy)/(dx)=1+x+y+x y

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

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

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  4. Solve the following differential equation: 5(dy)/(dx)=e^x y^4

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

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  6. (e^y+1)cosx dx+e^ysinx dy=0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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