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Find the equation of the curve passing through the point (1, 1) whose differential equation is `x dy =(2x^2+1)dx(x!=0)`.

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To find the equation of the curve passing through the point (1, 1) whose differential equation is given by \( x \, dy = (2x^2 + 1) \, dx \), we can follow these steps: ### Step 1: Rearrange the Differential Equation We start with the given differential equation: \[ x \, dy = (2x^2 + 1) \, dx \] We can rearrange this to isolate \( dy \): ...
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NCERT-DIFFERENTIAL EQUATIONS-SOLVED EXAMPLES
  1. Show that the differential equation xcos(y/x)(dy)/(dx)=ycos(y/x)+xis ...

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  2. Find the equation of a curve passing through the point (2, 3), given ...

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  3. Find the equation of the curve passing through the point (1, 1) whose...

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  4. Find the general solution of the differential equation (dy)/(dx)-y=co...

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  5. Show that the family of curves for which the slope of the tangent at ...

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  6. Form the differential equation representing the family of ellipses ha...

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  7. Form the differential equation of the family of circles touching the ...

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  8. Form the differential equation representing the family of curves y = ...

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  9. Form the differential equation representing the family of curves y = ...

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  10. Verify that the function y=e^(-3x)is a solution of the differential eq...

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  11. Verify that the functiony = a cos x + b sin x, where, a, b in Ris a ...

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  12. Find the order and degree, if defined, of each of the following differ...

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  13. Form the differential equation representing the family of parabolas h...

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  14. Find the general solution of the differential equation (dy)/(dx)=(x+1...

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  15. Solve the differential equation (tan^(-1)y-x)dy=(1+y^2)dx.

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  16. Verify that the function y=c1e^(a x)cosb x+c2e^(a x)sinb x, where c1...

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  17. Form the differential equation of the family of circles in the second...

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  18. Find the particular solution of the differential equation log ((dy)/(d...

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  19. Solve the differential equation (x dy-y dx)ysin(y/x)=(y dx+x dy)xcos(...

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  20. Find the general solution of the differential equation x(dy)/(dx)+2y=...

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