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Find the equation of the curve passing t...

Find the equation of the curve passing through the point `(0,1),` if the slope of the tangent to the curve at any point `(x,y),` is equal to the sum of `x` coordinate and product of `x` coordinate and `y` coordinate of that point.

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The correct Answer is:
`y = -1 + 2e^((x^(2))/(2))`
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NCERT TAMIL-DIFFERENTIAL EQUATIONS-MISCELLANEOUS EXERCISE
  1. Find the equation of the curve passing through the point (0,1), if the...

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  2. For each of the differential equations given below, indicate its order...

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

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

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  5. Prove that x^(2)-y^(2)=c(x^(2)+y^(2))^(2) is the general solution of d...

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

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  7. Find the general solution of the differential equation (dy)/(dx)+sqrt(...

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

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

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

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

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

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

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  14. Find a particular solution of the differential equation (dy)/(dx)+ycot...

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

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  16. The population of a village increases continuously at the rate proport...

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

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

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

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