Question

2) y = \frac{1}{(x^2 + c)} is a one-parameter family of solutions of the first-order DE $y' + 2xy^2 = 0$. Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(-3) = \frac{1}{2} y = \frac{-1}{6} Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.) Give the largest interval I over which the solution is defined for the given initial condition. (Enter your answer using interval notation.) 3) In this problem, $y = c_1e^x + c_2e^{-x}$ is a two-parameter family of solutions of the second-order DE $y'' - y = 0$. Find $c_1$ and $c_2$ that following initial conditions. (Your answers will not contain a variable.) y(1) = 0, y'(1) = e $c_1 = \frac{1}{2}$ $c_2 = \frac{-e^2}{2}$ Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. y = $e^x - e^{-x}$

          2)
y = \frac{1}{(x^2 + c)} is a one-parameter family of solutions of the first-order DE $y' + 2xy^2 = 0$. Find a solution of the first-order IVP
consisting of this differential equation and the given initial condition.
y(-3) = \frac{1}{2}
y = \frac{-1}{6}
Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)
Give the largest interval I over which the solution is defined for the given initial condition. (Enter your answer using interval notation.)
3)
In this problem, $y = c_1e^x + c_2e^{-x}$ is a two-parameter family of solutions of the second-order DE $y'' - y = 0$. Find $c_1$ and $c_2$ that
following initial conditions. (Your answers will not contain a variable.)
y(1) = 0, y'(1) = e
$c_1 = \frac{1}{2}$
$c_2 = \frac{-e^2}{2}$
Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.
y = $e^x - e^{-x}$

2)
y = (1)/((x^2 + c)) is a one-parameter family of solutions of the first-order DE y' + 2xy^2 = 0. Find a solution of the first-order IVP
consisting of this differential equation and the given initial condition.
y(-3) = (1)/(2)
y = (-1)/(6)
Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)
Give the largest interval I over which the solution is defined for the given initial condition. (Enter your answer using interval notation.)
3)
In this problem, y = c1e^x + c2e^-x is a two-parameter family of solutions of the second-order DE y” - y = 0. Find c1 and c2 that
following initial conditions. (Your answers will not contain a variable.)
y(1) = 0, y'(1) = e
c1 = (1)/(2)
c2 = (-e^2)/(2)
Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.
y = e^x - e^-x

Added by Scott P.

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