Question

solve for differential equation =

don't spam if you don't know answer.​

Answer 1

Answer:

Cancel xx on both sides.

x+{y}^{2}=2yxy

x+y

2

=2yxy

2 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

a

x

b

=x

a+b

.

x+{y}^{2}=2{y}^{2}x

x+y

2

=2y

2

x

3 Subtract {y}^{2}y

2

from both sides.

x=2{y}^{2}x-{y}^{2}

x=2y

2

x−y

2

4 Factor out the common term {y}^{2}y

2

.

x={y}^{2}(2x-1)

x=y

2

(2x−1)

5 Divide both sides by 2x-12x−1.

\frac{x}{2x-1}={y}^{2}

2x−1

x

=y

2

6 Take the square root of both sides.

\pm \sqrt{\frac{x}{2x-1}}=y

±

2x−1

x

=y

7 Switch sides.

y=\pm \sqrt{\frac{x}{2x-1}}

y=±

2x−1

x