Find the solution for which y = 6 when x = 0.

Question

Solve the differential equation using the technique of separation of variables

dy/dx = (x + 5x²)/y⁴

Find the solution for which y = 6 when x = 0.

y = ________

Answer 1

dy/dx = (x + 5x²) / y⁴

y⁴dy = (x + 5x²)dx

∫ y⁴dy = ∫ (x + 5x²)dx

(1/5)y⁵ = (1/2)x² + (5/3)x³ + C

Since y = 6 when x = 0, C = 1555.2.

y⁵ = (5/2)x² + (25/3)x³ + 7776

So, y = [(5/2)x² + (25/3)x³ + 7776]^1/5