1. Find the general solution (or as close as you can come to it) for the following differential
equations, using separation of variables.
(a) dy/dt = 2y − 1
(b) dy/dt = t^2y^3

Question

1. Find the general solution (or as close as you can come to it) for the following differential
equations, using separation of variables.
(a) dy/dt = 2y − 1
(b) dy/dt = t^2y^3

amistre64 · Answer

separation is just splitting up same variables on same sides

amistre64 · Answer

$$\frac{dy}{dt}=2y-1$$
$$dy=(2y-1)dt$$
$$(2y-1)^{-1}dy=dt$$
$$\int((2y-1)^{-1}dy=dt)$$

anonymous · Answer

so the asnwer would be $$y=\sqrt[3]{pmAe^(t^3/3)}$$

anonymous · Answer

that e^(t^3/3)

amistre64 · Answer

$$\int((2y-1)^{-1}dy=dt)$$
$$\frac{1}{2}ln|2y-1|=t+C$$
$$ln|2y-1|=2t+C$$
$$2y-1=\pm C*exp(2t)$$
$$y=\pm \frac{Ce^{2t}+1}{2}$$
is what I get