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Show that the general solution of the di...

Show that the general solution of the differentia equation `(dy)/(dx)+(y^2+y+1)/(x^2+x+1)=0` is given by `x+y+1=A(1-x-y-2x y)` where A is a parameter.

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RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Solve the initial value problem: (x+1)(dy)/(dx)=2e^(-y)-1,\ y(0)=0

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  2. Solve the initial value problem: y-x(dy)/(dx)=2(1+x^2(dy)/(dx)),\ y(1)...

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  3. Show that the general solution of the differentia equation (dy)/(dx)...

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  4. Solve the following differential equation log ((dy)/(dx))=3x+4y

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  5. In a bank, principal increases continuously at the rate of 5% per y...

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  6. Find the equation of the curve passing through the point (0, -2) gi...

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  7. At any point (x, y) of a curve, the slope of the tangent is twice t...

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

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

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

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  11. Solve the following differential equation: xcosy\ dy=(x e^xlogx+e^x)dx

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

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  13. Solve the following differential equation: x(dy)/(dx)+coty=0

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

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  15. Solve the following differential equation: cosxcosy(dy)/(dx)=-sinxsiny

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

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

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

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

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

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