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anonymous
 4 years ago
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
anonymous
 4 years ago
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

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dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{dy}{dt} 2y = 1\] find integrating factor \[e^{\int\limits_{}^{}2} = e^{2t}\] \[\frac{dy}{dt}e^{2t} 2e^{2t}y = e^{2t}\] \[(e^{2t}y)\frac{d}{dt} = e^{2t}\] integrate both sides with respect to t \[e^{2t}y = \frac{1}{2}e^{2t} + C\] \[y = \frac{1}{2} +Ce^{2t}\]

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{dy}{dt} = t^{2}y^{3}\] separate variables \[\frac{dy}{y^{3}} = t^{2} dt\] integrate both sides \[\frac{1}{2y^{2}} = \frac{t^{3}}{3}+C\] \[2y^{2} = \frac{3}{Ct^{3}}\] \[y = \sqrt{\frac{3}{C2t^{3}}}\]
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