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

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