Question

solve the given initial value problem. y(cos2t)e^ty - 2(sin2t)e^ty + 2t + (t(cos2t)e^ty - 3) dy/dt = 0, y(0)=0

Answer #1

Doubt in any step then comment below. I will explain you.

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Here this equation is exact differential equation , we easily show this ..

Answer is in last closed bracket....

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t^(13) (dy/dt) +2t^(12) y =t^25 with t>0 and y(1)=0
(y'-e^-t+4)/y=-4, y(0)=-1

1. Solve the given initial value problem. dy/dt = (t^3 +
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2. We know from Newton’s Law of Cooling that the rate at which a
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The differential equation corresponding to this situation is given
by y' = k(M − y) where k is a positive constant. The solution to
this equation is given...

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7 =

Solve the initial value problem 8(t+1)dy/dt−6y=12t, for t>−1
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Find the general solution to the given differential
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1. Solve the following initial value problem using Laplace
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d^2y/dt^2+ y = g(t) with y(0)=0 and dy/dt(0) = 1 where g(t) = t/2
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1)Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1. Let af/ax = (x + y)2 =
x2 + 2xy + y2. Integrate each term of this
partial derivative with respect to x, letting
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f(x, y) = + h(y)
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(6y + 2t − 3)
dt + (8y + 6t
− 1) dy...

1) Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1
Let af/ax = (x + y)2 = x2 + 2xy +
y2.
Integrate each term of this partial derivative with respect to
x, letting h(y)
be an unknown function in y.
f(x, y) = + h(y)
Find the derivative of h(y).
h′(y) =
Solve the given initial-value problem.
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(6y + 2t − 3)
dt...

solve the given initial value problem
dx/dt=7x+y x(0)=1
dt/dt=-6x+2y y(0)=0
the solution is x(t)= and y(t)=

Initial value problem : Differential equations:
dx/dt = x + 2y
dy/dt = 2x + y
Initial conditions:
x(0) = 0
y(0) = 2
a) Find the solution to this initial value problem
(yes, I know, the text says that the solutions are
x(t)= e^3t - e^-t and y(x) = e^3t + e^-t
and but I want you to derive these solutions yourself using one
of the methods we studied in chapter 4) Work this part out on paper
to...

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