The solution curve, of the differential equation 2 y d x d y + 3 = 5 d x d y , passing through the point ( 0 , 1 ) is a conic, whose vertex lies on the line:

Question

The solution curve, of the differential equation 2 y d x d y ​ + 3 = 5 d x d y ​ , passing through the point ( 0 , 1 ) is a conic, whose vertex lies on the line:

TestHub · Accepted Answer

​ ( 2 y − 5 ) d x d y ​ = − 3 ( 2 y − 5 ) d y = − 3 d x 2 ⋅ 2 y 2 ​ − 5 y = − 3 x + λ ​ ∵ Curve passes through ( 0 , 1 ) ⇒ λ = − 4 ∵ Curve will be ( y − 2 5 ​ ) 2 = − 3 ( x − 4 3 ​ ) ∴ Vertex of parabola will be ( 4 3 ​ , 2 5 ​ ) ∵ 2 x + 3 y = 9

Mathematics - Differential Equation Question with Solution | TestHub

Options:

Doubts & Discussion