Solve the separable differential equation dydx02y and find t

Solve the separable differential equation: dy/dx=0.2y, and find the particular solution satisfying the initial condition y(0)=-9

y(x)=???

separate variables dy/y = 0.2 dx integrate ln|y| = 0.2x +C exponentiate y = e^{0.2x+C} = K e^{0.2x} Choose K to satisfy the initial condition -9 = K e^{0} The solution is y(x) = -9 e^{0.2 x}