Question

Can someone please solve this Differential Equation? math teacher didn’t explain this to me so be sure to include steps taken !

Answer 1

√y = ¼ x² + 2

y = (¼ x² + 2)²

Explanation:

dy / dx = x √y

Separate the variables:

dy / √y = x dx

Change radical to exponent:

y^-½ dy = x dx

Integrate both sides using power rule:

2 y^½ = ½ x² + C

2√y = ½ x² + C

Substitute initial condition:

2√9 = ½ (2)² + C

6 = 2 + C

C = 4

Therefore:

2√y = ½ x² + 4

√y = ¼ x² + 2

y = (¼ x² + 2)²