How do you go about solving the differential equation of the following form?dydt+y(t)=k, where k is a constant.Would the method of integrating factors typically used for the following forms work:dydt+a(t)y=b(t)

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Mey9ci0 · Accepted Answer

Step 1Yes, integrating factors will work, here:dydt+y(t)&amp;nbsp;=ke∫P(t)&amp;nbsp;dt&amp;nbsp;=etet&amp;nbsp;dydt+et&amp;nbsp;y(t)&amp;nbsp;=k&amp;nbsp;etddt[et&amp;nbsp;y(t)]&amp;nbsp;=k&amp;nbsp;etet&amp;nbsp;y(t)&amp;nbsp;=k&amp;nbsp;et+Cy(t)&amp;nbsp;=k+C&amp;nbsp;e−t.Step 2To check, you plug back into the DE:y˙(t)=−Ce−t,Therefore&amp;nbsp;y˙(t)+y(t)=−Ce−t+k+Ce−t=k, as required.

ditumpasz9xj · Accepted Answer

Explanation:You can just integrate by passing everything except the derivative to the other side, i.edydt=k−a(t)⇒y=∫(k−a(t)) dt=kt−A(t)+Cwhere A(t) is a primitive of a(t) and C is the integration constant.

How do you go about solving the differential

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