To solve the linear equation \(y'+P(x)y=Q(x)\), multiply both sides by the integrating factior \(\displaystyle{v}{\left({x}\right)}={e}^{{\int{P}{\left({x}\right)}{\left.{d}{x}\right.}}}\) and integrate both sides.

Question

asked 2021-05-26

Write the following first-order differential equations in standard form. \(\displaystyle{y}'={x}^{{{3}}}{y}+{\sin{{x}}}\)

asked 2021-05-22

Write the following first-order differential equations in standard form. \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}}={y}{x}{\left({x}+{1}\right)}\)

asked 2021-07-05

Write first-order differential equations that express the situation: The increase in the number of people who have heard a rumor in a town of population 20,00020,000 is proportional to
the product of the number PP who have heard the rumor and the number who have not heard the rumor at time tt .

asked 2021-06-10

Write first-order differential equations that express the situation: A student in an engineering course finds the rate of increase of his grade point average GG is directly proportional to the number NN of study hours/week and inversely proportional to the amount AA of time spent on online games .