NCERT Class 12-Mathematics: Chapter –9 Differential Equations Part 10

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Question 28:

Find the general solution of

Answer:

Question 29:

Find the equation of a curve passing through if the slope of the tangent to the curve at any point is

Answer:

It is given that, the slope of tangent to the curve at point

Which is homogeneous differential equation.

Put

On substituting these values in Eq. (i), we get

On integrating both sides, we get

Put LHS, we get

Since, the curve passes through the point

So, the required solution is

Question 30:

Find the equation of the curve through the point (1, 0) if the slope of tangent to the curve at any point is

Answer:

It is given that, slope of tangent to the curve at any point is

On integrating both sides, we get

Since, the given curve passes through point

The particular solution is