NCERT Class 12-Mathematics: Chapter – 9 Differential Equations Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 6:

Find the differential equation of all non-horizontal lines in a plane.

The general equation of all non-horizontal lines in a plane is

.

Therefore,

Again, differentiating both sides w. r. t. y, we get

Question 7:

Find the equation of a curve whose tangent at any point on it, different from origin, has slope

Given

Integrating both sides, we get

Question 8:

Find the equation of a curve passing through the point if the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of P from the axis.

Let the equation of normal at

Therefore, the length of perpendicular from origin to is

Also distance between P and axis is . Thus, we get

Case I:

Integrating both sides, we get , Substituting , we get .

Therefore, is the equation of curve (not possible, so rejected) .

Case II: Substituting , we get

Integrating both sides, we get

. Substituting , , we get .

Therefore, is the required equation.

Question 9:

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