Question

equatien y=y/x+6x​/2-ln x​ Q2) Solve the following nonlinei DE by using an integratiny fuctor of the form m(x) or m(y), y′=−4x+3y²/2xy

Answer 1

To solve the nonlinear differential equation y′=−4x+3y²/2xy, we can use an integrating factor of the form m(x) or m(y). First, we rewrite the equation in standard form by multiplying both sides by 2xy.

Step-by-step explanation:

To solve the nonlinear differential equation y′=−4x+3y²/2xy, we can use an integrating factor of the form m(x) or m(y). First, we rewrite the equation in standard form by multiplying both sides by 2xy:

2xyy′=−4x(2xy)+3y²(2xy)

Simplifying, we get:

2xyy′+8x²y−6xy³ = 0

This nonlinear differential equation can be solved by using a change of variables. Let v = y², then we have:

2xyy′ + 8x²√v − 6xyv = 0

This equation can be now considered linear in terms of v.