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Find the particular solution of the dif...

Find the particular solution of the differential equation `(1 + e^(2x))dy + (1 + y^(2))e^(x)dx = 0`, given that y = 1 when x = 0

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The correct Answer is:
`tan^(-1) y + tan^(-1)(e^(x)) = (pi)/(2)`
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NCERT GUJARATI-DIFFERENTIAL EQUATIONS-MISCELLANEOUS EXERCISE
  1. For each of the differential equations given below, indicate its order...

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  2. For each of the exercises given below, verify that the given function...

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  3. Form the differential equation representing the family of curves give...

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  4. Prove the x^(2) - y^(2) = c (x^(2) + y^(2))^(2) is the general solutio...

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  5. Form the differential equation of the family of circles in the first q...

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  6. Find the general solution of the differential equation (dy)/(dx) + sqr...

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  7. Show that the general solution of the differential equation (dy)/(dx) ...

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  8. Find the equation of the curve passing through the point (0, (pi)/(4))...

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  9. Find the particular solution of the differential equation (1 + e^(2x)...

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

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  11. Find a particular solution of the differential equation (x - y)(dx + d...

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  12. Solve the differential equation [(e^(-2sqrtx))/(sqrtx) - (y)/(sqrtx)](...

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  13. Find a particular solution of the differential equation (dy)/(dx) + y...

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  14. Find a particular solution of the differential equation (x + 1)(dy)/(d...

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  15. The population of a village increases continuously at the rate propor...

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  16. The general solution of the differential equation (y dx - x dy)/(y ) =...

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  17. The general solution of a differential equation of the type (dy)/(dx)...

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  18. The general solution of the differential equation e^(x) dy + (y e^(x) ...

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