Solve the initial value problem $$\frac { \mathrm { dP } } { \mathrm { dt } } = 9 \mathrm { kP } ^ { 2 } , \mathrm { P } ( 0 ) = \mathrm { P } _ { 0 }$$
A) $P ( t ) = \frac { 9 P _ { 0 } } { 1 - 9 k P _ { 0 } t }$
B) $P ( t ) = \frac { P _ { 0 } } { 9 - 9 k P _ { 0 } t }$
C) $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { P } _ { 0 } } { 1 - \mathrm { kP } _ { 0 } \mathrm { t } }$
D) $P ( t ) = \frac { P _ { 0 } } { 1 - 9 k P _ { 0 } t }$

Question

Quizplus · Accepted Answer

To solve the differential equation, we separate variables and integrate both sides. The solution involves integrating $1/P^2$ on the left and $9k$dt on the right, leading to the solution where $P(t) = \frac{P_0}{1 - 9kP_0t}$, matching option D.

Solve the Initial Value Problem dPdt=9kP2,P(0)=P0\frac { \mathrm { dP } } { \mathrm { dt } } = 9 \mathrm { kP } ^ { 2 } , \mathrm { P } ( 0 ) = \mathrm { P } _ { 0 }dtdP​=9kP2,P(0)=P0​

Solve the Initial Value Problem $\frac { \mathrm { dP } } { \mathrm { dt } } = 9 \mathrm { kP } ^ { 2 } , \mathrm { P } ( 0 ) = \mathrm { P } _ { 0 }$