Solve.
-Solve the initial value problem $\frac { \mathrm { dP } } { \mathrm { dt } } = 7 \mathrm { kP } ^ { 2 } , \mathrm { P } ( 0 ) = \mathrm { P } _ { 0 }$
A) $P ( t ) = \frac { 7 P _ { 0 } } { 1 - 7 \mathrm { kP } _ { 0 } t }$
B) $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { P } _ { 0 } } { 1 - 7 \mathrm { kP } _ { 0 } \mathrm { t } }$
C) $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { P } _ { 0 } } { 7 - 7 \mathrm { kP } _ { 0 } \mathrm { t } }$
D) $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { P } _ { 0 } } { 1 - \mathrm { kP } _ { 0 } \mathrm { t } }$

Question

Quizplus · Accepted Answer

The differential equation $\frac { \mathrm { dP } } { \mathrm { dt } } = 7 \mathrm { kP } ^ { 2 }$ can be solved using separation of variables. Integrating both sides with respect to their respective variables and applying the initial condition $P(0) = P_0$ leads to the solution $P(t) = \frac { P_0 } { 1 - 7 kP_0 t }$, which matches choice B.

Solve -Solve the Initial Value Problem dPdt=7kP2,P(0)=P0\frac { \mathrm { dP } } { \mathrm { dt } } = 7 \mathrm { kP } ^ { 2 } , \mathrm { P } ( 0 ) = \mathrm { P } _ { 0 }dtdP​=7kP2,P(0)=P0​

Solve
-Solve the Initial Value Problem $\frac { \mathrm { dP } } { \mathrm { dt } } = 7 \mathrm { kP } ^ { 2 } , \mathrm { P } ( 0 ) = \mathrm { P } _ { 0 }$