\(dy/(dt)+Py=Q\)

Hence P=2, Q=1

\(I.F.= e^{\int Pdt}\)

\(= e^{\int 2dt}\)

\(= e^{2t}\)

\(y*I.F.= \int Q*I.F.\)

\(ye^{2t}= \int 1(e^{2t})\)

\(ye^{2t}= e^{2t}/2+C\)

\(y=1/2+Ce^{-2t}\)

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 2021-05-01

Solve differential equation
\(xy'+2y= -x^3+x, \ y(1)=2\)

asked 2021-03-07

Solve differential equation \(\frac{\cos^2y}{4x+2}dy= \frac{(\cos y+\sin y)^2}{\sqrt{x^2+x+3}}dx\)

asked 2021-05-03

How do you solve linear first-order differential equations?

asked 2021-01-02

Solve the Differential equations

\(\frac{(d^{2}y)}{dt^{2}}+4\frac{dy}{dt}+3y=e^{-t}\)

asked 2021-03-07

Solve differential equation \((1+y^2+xy^2)dx+(x^2y+y+2xy)dy=0\)

asked 2021-05-26

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

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 .

asked 2020-12-24

Solve differential equation
\(\displaystyle{2}{x}{y}-{9}{x}^{{2}}+{\left({2}{y}+{x}^{{2}}+{1}\right)}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={0},\ {y}{\left({0}\right)}=-{3}\)