Q. 74.0( 4 Votes )

# Form the differential equation corresponding to y^{2} – 2 ay + x^{2} = a^{2} by eliminating a.

Answer :

y^{2} – 2 a y + x^{2} = a^{2}

On differentiating, with respect to x we get,

Putting this value of a in the given equation, we get,

⇒ y^{2}y'^{2} – 2y^{2}y'^{2} – 2xyy' + x^{2}y'^{2} = y^{2} y'^{2} + 2xyy' + x^{2}

⇒ y^{2}y'^{2} – 2y^{2}y'^{2} – 2xyy' + x^{2}y'^{2} – y^{2} y'^{2} – 2xyy' – x^{2} = 0

⇒ – 4xyy' + y'^{2}x^{2} – x^{2} – 2y'^{2}y^{2} = 0

⇒ y’^{2}(x^{2} – 2y^{2}) – 4xyy’ – x^{2} = 0

So, y’^{2}(x^{2} – 2y^{2}) – 4xyy’ – x^{2} = 0

Rate this question :

Solve the differential equation given that when

Mathematics - Board PapersThe general solution of e^{x} cosy dx – e^{x} siny dy = 0 is:

The differential equation represents:

Mathematics - ExemplarForm the differential equation of the family of parabolas having vertex at the origin and axis along positive y–axis.

Mathematics - Board PapersSolve the differential equation

Mathematics - ExemplarGiven that and y = 0 when x = 5.

Find the value of x when y = 3.

Mathematics - ExemplarFind the equation of a curve passing through origin and satisfying the differential equation

Mathematics - Exemplar