Differential Equations Answers

Find the general solution of the differential equation y" + 16y = 2 sec(4t) tan(4t)

Select one:

O none of the given answers is true

y = ci cos(4t) + c2 sin(4t) + ,t cos(4t) - sin(4t) In | cos(4t) |

y = ci cos(4t) + c2 sin(4t) - t cos(4t) + sin(4t) In | cos(4t) |

y = ci cos(4t) + c2 sin (4t) -

7t sin(4t) - - cos(4t) In | sin(4t) |

y = ci cos(4t) + C2 sin(4t) + ,t sin(4t) + - cos(4t) In | sin(4t)|

If yp = uj (t) cos(2t) + u2(t) sin(2t) is a particular solution of the differential equation

y" + 4y= csc(2t) cot(2t), then u, (t) =

Select one:

O none of the given answers is true

O Lt + - cot(2t)

O _ In | sin(2t) |

O

_ In | sin(2t) |

O

cot (2t)

1. Show whether or not the following differential equations are separable:

1.1 "\\frac{dy}{dx}=\\frac{x+1}{y-1}"

1.2 "\\frac{dy}{dx}=\\frac{ye^{x}+y}{x^2+2}"

1.3 "\\frac{ds}{dt}=t\\ln(s^{2t})+8t^2"