Question

Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor.4xy dx (4y 6x2) dy

Answer 1

Answer:

y=1/6 · ln |x|+c .

Step-by-step explanation:

From Exercise we have the differential equation

4xy dx= (4y6x²) dy.

We calculate the given differential equation, we get

4xy dx= (4y6x²) dy

xy dx=6yx² dy

6 dy=1/x dx

∫ 6 dy=∫ 1/x dx

6y=ln |x|+c

y=1/6 · ln |x|+c

Therefore, we get that the solution of the given differential equation is

y=1/6 · ln |x|+c .