Using separation of variables, solve the differential equation,

Question

Using separation of variables, solve the differential equation,

(3+𝑥^10)(𝑑𝑦/𝑑𝑥) = 𝑥^9/𝑦

Use C to represent the arbitrary constant.

y^2=_____________

Answer 1

Rewrite as y dy = x^9/3+x^10 dx

As (3+x^10)' = 10x^9, we solve

y^2/2 = 1/10 ln(3+x^10) + C

y^2 = 1/5 ln(3+x^10) + 2C

Since C is any constant, y^2 = 1/5 ln(3+x^10) + C