The general solution of the equation: t?y" + 2ty' = 0 is y = c1+ c2/t. You use the variation of parameters method to look for a solution of ty"+2ty' = sin(t) in the form y = u1 (t)+u2(t)/t. Then u1 and u2 should satisfy the system: (a) u1 + u2/t = 0, u – uz/t² = sin(t) (b) u + uz/t = sin(t), u – uz/t² = 0 (c) u + u2/t = 0, u2 = – sin(t) (d) u + u/t = 0, u = -t sin(t)

Solve: y=sec3(2-3x)

5. Okay, time for some mathematics. We're going to focus on the interactions between the hares and their main predators, the lynx. The tool we need is differential equations (last seen when we talked about the S-I-R disease model). We will let H(t) be the density of hares at time t, and L(t) the density of lynx at time t. Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hares lead to more hares and faster growth. This gives us the differential equation (trust me): HP = aH dt where a is a positive constant. Second we assume that, if there are no hares around, the lynx starve and thus their numbers decay exponentially. This gives us: TP = -bL dt

Find a general solution of the system: x' =1²2 =21* L2

) Find the general solution to y"" + 10y" + 34y' = 0. In your answer, use C₁, C₂ and c3 to denote arbitrary constants and x the independent variable. help (equations)