Find the general solution to the differential equation dudt+1t+1u=2\frac{du}{dt} + \frac{1}{t+1} u = 2dtdu+t+11u=2.
u(t)=t+1+Ct+1u(t) = t + 1 + \frac{C}{t+1}u(t)=t+1+t+1C
u(t)=(t+1)+Ct+1u(t) = (t+1) + \frac{C}{t+1}u(t)=(t+1)+t+1C
u(t)=t+1+C(t+1)u(t) = t + 1 + C(t+1)u(t)=t+1+C(t+1)
u(t)=2(t+1)+Ct+1u(t) = 2(t+1) + \frac{C}{t+1}u(t)=2(t+1)+t+1C