Mathematics
Mathematics, 01.08.2019 10:30, mandilynn22

Find the solution to initial value problem d2ydt2−10dydt+25y=0, y(0)=4,y′(0)=5

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Mathematics, 15.07.2019 18:20, Kingdcn6261
6. consider the following initial value problem: y 000 − y = 0 , y(0) = 1 , y0 (0) = 0 , y00(0) = 0 . (a) assume there is a solution of the form y(t) = e rt, and plug this back in and solve for r. use this to write the general solution. [hint: the equation r 3 = 1 has 3 distinct solutions over c, called the 3rd roots of unity: r1 = e 0πi/3 = 1, r2 = e 2πi/3 , and r2 = e 4πi/3 .] (b) from here, you could solve the initial value problem by plugging in the initial conditions, but you’ll get a system of three equations with three unknowns, and involving complex numbers. here’s another way: look for a power series solution, y(t) = x∞ n=0 ant n . plug this back into the ode and find the recurrence relation for the coefficients. (c) compute an for n ≤ 10, and once you see the pattern, write down the general solution to the ode as a power series. [hint: it should look familiar! ] (d) write down a basis for the solution space. (e) plug in the initial conditions and find the particular solution to the ivp. (f) solve a similar initial value problem:
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Mathematics, 01.08.2019 10:30, firstone04kr
Find the solution to the boundary value problem: d2ydt2−7dydt+10y=0, y(0)=6,y(1)=3
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Mathematics, 01.10.2019 01:30, mayaparness
Problem 1: consider the initial value problem y' + (1/4)y = 3 + 2cos(2t), y(0) = 0. (a) find the solution of this initial value problem and describe its behavior for large t. (b) determine the value of t for which the solution first intersects the line y = 12. problem 2: find the value of latex: y_0y 0 for which the solution of the initial value problem y' - y = 1+ 3sin(t), y(0) = latex: y_0
Answers: 3
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Mathematics, 08.10.2019 00:30, cpadoc7567
Consider the following initial value problem 5 points (1 + t) y’ = t y (4 – y), y(0) = y0 > 0. a) solve the initial value problem and find its general solution. b) determine how the solution behaves as t ø¶. c) if the initial value y0 = 2, find the time t when the solution first reaches the value 3.99.
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Find the solution to initial value problem d2ydt2−10dydt+25y=0, y(0)=4,y′(0)=5...

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