System & Surroundings

1.2 First-order linear differential equations

1.2 First-order linear differential equations 1) Definition of general first-order linear differential equation \[\frac{dy}{dt}+a(t)y=b(t)\] nonhomogeneous first-order linear differential equation for b(t)≠0 e.g. \[\frac{dy}{dt}=y^{2}+sin(t)\] \[\frac{dy}{dt}=cos(y)+t\] are nonlinear equations for y^2 and cos(y) 2) Definition of homogeneous first-order linear differential equation \[\frac{dy}{dt..