Question

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.

Answer 1

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: $xy' +2y=4x^{2}$, it given a solution function:

$y=x^{2}+cx^{2}$

Factorating the function: $y=x^{2}(1+c)$

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

When x = 10, y = 2:

$2=10^{2}(1+c)$

$1+c=\frac{2}{100}$

$1+c=0.02$

c = -0.98

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