Find the complete solution of the given differential equation <mrow class="MJX-TeXAtom-ORD">

Villaretq0

Villaretq0

Answered question

2022-06-13

Find the complete solution of the given differential equation
d y d x = 3 x 1 + y 2 y
I know how to solve it if the right side didn't contain either x or y, but I can't think of a way to arrange them. I think I should solve for y, but I'm not sure. Could anyone show me the solution?

Answer & Explanation

hopeloothab9m

hopeloothab9m

Beginner2022-06-14Added 25 answers

Explanation:
Arrange as follows:
y   d y 1 + y 2 = 3 x   d x = 1 2 d ( y 2 ) 1 + y 2 = 3 2 d ( x 2 )
d ( y 2 ) 1 + y 2 = 3 d ( x 2 )
2 1 + y 2 = 3 x 2 + C
tr2os8x

tr2os8x

Beginner2022-06-15Added 10 answers

Explanation:
Just try to separate the y and x sides. Multiply both sides by y and divide both sides by 1 + y 2 to get the ys on the left side and then multiply both sides by dx to get the xs on the right side.
y 1 + y 2 d y = 3 x d x
Now integrate both sides.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?