Answer: 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: [tex]xy' +2y=4x^{2}[/tex], it given a solution function:
[tex]y=x^{2}+cx^{2}[/tex]
Factorating the function: [tex]y=x^{2}(1+c)[/tex]
So, to determine constant c, use the initial condition:
When x = 10, y = 2:
[tex]2=10^{2}(1+c)[/tex]
[tex]1+c=\frac{2}{100}[/tex]
[tex]1+c=0.02[/tex]
c = -0.98
Constant c that satisfies the initial condition is c = -0.98
