Mathematics - Differential Equation Question with Solution | TestHub

$\frac{d(p(t))}{dt}=\frac{1}{2}p(t)-450$ $\frac{d(p(t))}{dt}=\frac{p(t)-900}{2}$ $2\int \frac{d(p(t))}{p(t)-900}=\int dt$ $2\ln |p(t)-900|=t+c$ $t=0\Rightarrow 2\ln 50=0+c\Rightarrow c=2\ln 50$ $\therefore 2\ln |\mathrm{p}(\mathrm{t})-900|=\mathrm{t}+2\ln 50$ $P(\mathrm{t})=0\Rightarrow 2\ln 900=\mathrm{t}+2\ln 50$ $t=2(\ln 900-\ln 50)=2\ln \left(\frac{900}{50}\right)=2\ln 18$.