Use Euler's method with step size 0.3 to compute the approximate y-values y(0.3) and y(0.6), of the solution of the initial-value problem y = −1+3x - 4y, y(0) = -3. y(0.3) y(0.6) = = "

Given y₁ (x) 1 Order to find a second solution. e³x 3x is a solution to the given equation, use the Method of Reduction of -= = xy'' — (6x − 2)y' + (9x − 6)y = 0, x > 0 - Give your answer in the simplest form (i.e., no coefficients) Y₂(x) =

The initial condition was at time 0 there was 4 inches of snow (h(0)=4), and with our snowfall rate of 3/5 and snow removal rate of 9/20h the LOWEST the height of snow on the ground could go is 4/3 inches. But i'm wondering, given our initial condition of h(0)=4, Is there any combination of snowfall rate and snow removal rate that could allow the height of snow on the ground to approach zero? For instance, if we made our equation dH/dt=(1/5)-(4/5)*h we could get the lowest snow height to under half an inch...but are there any conditions in which we could get it to approach zero? If not, what's the lowest we could get it and the process for finding such a value? Please explain. Thank you

Solve the initial value problem. 2x²-x dy dx O B. = -x-5 (x + 1)(y + 1)' Begin by separating the variables. Choose the correct answer below. O C. A. (y + 1)dy=- y(1)=2 2x²-x-5 x²(x+1) x²(x+1) dy 2x²-x-5 -= dx x²(x+1)(y+1) -dx 2x² 1 -dy= -dx -X-5 y + 1 D. The equation is already separated. The solution is (Type an implicit solution. Type an equation using x and y as the variables.)

Convert the following equation to the form of a Sturm-Louville equation3x^2 y´´ (x) + 4xy´ + 6y(x)  +   λy(x)  =0  ,  x>0

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