Solve the vector initial-value problem for y t by integrating and using the initial conditions to find the constants of integration . y ″ t = i + e t j , y 0 = 2 i , y ′ 0 =j
Solve the vector initial-value problem for y t by integrating and using the initial conditions to find the constants of integration . y ″ t = i + e t j , y 0 = 2 i , y ′ 0 =j
Solve the vector initial-value problem for
y
t
by integrating and using the initial conditions to find the constants of integration.
y
″
t
=
i
+
e
t
j
,
y
0
=
2
i
,
y
′
0
=j
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
The velocity of a particle moving in the plane has components
dx
= 12t – 312 and-
dt
dy
= In(1 + (t – 4)*)
dt
At time t = 0, the position of the particle is (-13, 5). At time t= 2, the object is at point P with
x-coordinate 3.
Find the speed of the particle and its acceleration vector at t= 2.
Find the y-coordinate of P.
Write an equation for the tangent line to the curve at P.
SOLVE THE DE
1. Find out the integrating factor and solve: x dy + (3x + 1) y dx
= e-3dx.
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