Answer both Seperation of Varaible questions correctly to Earn Best Answer!?

Question

Find the solution to the differential equation, subject to the given initial condition.

1) dy/dt= y/4+t, y(0)=4
y(t)=?

2) (dy/dx)+(y/9)= 0, y(0)=10
y(x)=?

Answer 1

1) The variables separate as dy/y = dt/(4 + t). We integrate to get ln(y) = ln(4 + t) + C and exponentiate to find y = (e^C)*(4 + t). Using y = 4 when t = 0 we find e^C = 1, so y = 4 + t is the solution.

2) Separation yields dy/y = -dx/9, so ln(y) = -x/9 + C, and
y = (e^C)*e^(-x/9). The initial condition gives us e^C = 10, so y = 10e^(-x/9).