What is the particular solution to the differential equation....

Question

dy/dx=(y)^2/2x+3 with the initial condition y(-1)=5?

Can someone please show work with their answer? Thank you.

Answer 1

WE separate variables and integrate: ∫dy/y² = ∫dx/(2x + 3); -1/y = 1/2lnI2x + 3I + C; If x = - 1 y = 5;

so, - 1/5 = 1/2ln1 + C; C = -1/5;-1/y = 1/2lnI2x + 3I - 1/5