The functions y=x2+cx2 are all solutions of equation: xy′+2y=4x2, (x>0). Find the constant c which produces a solution which also satisfies the initial condition y(10)=2.

c = -0.98

Step-by-step explanation: Differential equation of first order is an equation involving differentiable function and its derivative.

For the differential equation: , it given a solution function:

Factorating the function:

So, to determine constant c, use the initial condition:

When x = 10, y = 2:

c = -0.98

Constant c that satisfies the initial condition is c = -0.98