Is $P = 250 + C e ^ { 0.2 t }$ a solution to the differential equation $\frac { d P } { d t } + 0.2 P = 50$ (for some constant C)?

Name: Is $P = 250 + C e ^ { 0.2 t }$ a solution to the differential equation $\frac { d P } { d t } + 0.2 P = 50$ (for some constant C)?
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Question

Quizplus · Accepted Answer

Substituting $P = 250 + C e^{0.2t}$ into the differential equation does not satisfy it, as the left side becomes $\frac{dP}{dt} + 0.2P = 0.2Ce^{0.2t} + 0.2(250 + Ce^{0.2t})$, which simplifies to $50 + 0.4Ce^{0.2t}$, not equal to 50.

Is P=250+Ce0.2tP = 250 + C e ^ { 0.2 t }P=250+Ce0.2t

Is $P = 250 + C e ^ { 0.2 t }$