Question

solve the following initial value problem x^{'} = 2xy
y^{'} = y -2t +1 x(0) = x_{0} y(0) =
y_{0}

Answer #1

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)
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(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.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt...

Consider the following Initial Value Problem (IVP)
y' = 2xy, y(0) = 1.
Does the IVP exists unique solution? Why? If it does, ﬁnd the
solution by Picard iteration with y0(x) = 1.

Solve the following initial value problem using Laplace
transform
y"+2y'+y=4cos(2t) When y(0)=0 y'(0)=2
Thankyou

Solve the given initial-value problem. d2x dt2 + 4x = −5 sin(2t)
+ 9 cos(2t), x(0) = −1, x'(0) = 1

Use Laplace Transforms to solve the given initial value problem
y''-4y'+4y=t^3e6(2t) y(0)=1 and y'(0)=-2

Solve the initial value problem below using the method of
Laplace transforms. y"+11y'+30y=280e^2t, y(0)=1, y'(0)=32

solve the following initial value problem
y(3)+y'' = 5x + 8e-x, y(0)=1, y'(0)=0,
y''(0)=1

Solve the following initial value problem, showing all work.
Verify the solution you obtain.
y''-2y'+y=0;
y0=1,
y'0=-2.

Solve the initial value problem
x′=−3x−y,
y′= 13x+y,
x(0) = 0,
y(0) = 1.

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