Find the particular solution of the differential equation given that y = 0 when x = 0.

Using properties of determinants, prove that:

If x = cost(3 - 2 cos² t) and y = sin t(3 - 2 sin² t), find the value of at

Find the value of p, so that the lines and are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, –4) and parallel to line l₁.

If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum, when the angle between them is 60°.