Question: Consider the following differential equation \[2xydx+\left( 1+{{x}^{2}} \right)dy=0\] (3) (a) (5 points) Determine whether the equation in (3) is linear (in x or y...

Question: Solve each of the initial value problems below and indicate the method you use a- \(y’-2xy=2{{x}^{2}}{{e}^{{{x}^{2}}}},\,\,\,y\left( 0 \right)=5\) b- \(\left( 1-{{x}^{4}} \right)y’=\frac{{{x}^{3}}}{y},\,\,\,y\left( 0 \right)=2\)

Question: Polonium-210 is a radioactive element with a half life of 140days. Assume that 20 milligrams of the element are placed in a lead container...

Question: A tank with a 1000-gal capacity initially contains 500gal of water that is polluted with 50lbs of particulate matter. At time t=0, pure water...