3) Solve the initial value problems c) R′ + (R/t) = (2/(1+t2 )) , R(1) =...

3) Solve the initial value problems

c) R′ + (R/t) = (2/(1+t² )) , R(1) = ln 8.

e) ) cos θv′ + v = 3 , v(π/2) = 1.

5) Express the general solution of the equation x ′ = 2tx + 1 in terms of the erf function.

7) Solve x ′′ + x ′ = 3t by substituting y = x ′

9) Find the general solution to the differential equation x ′ = ax + b, where a and b are constants, first by separation of variables, and second by integrating factors

Expert Solution

Colby Messinger answered 2 years ago

Solve listed initial value problems by using the Laplace Transform: 3. yll + 4y = t −...

Solve listed initial value problems by using the Laplace Transform: 3. yll + 4y = t − 1, y(0) = 1, yl(0) = −1

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Consider the following vector function. r(t) =<3t, 1/2 t2, t2> (a) Find the unit tangent and...

Consider the following vector function. r(t) =<3t, 1/2 t2, t2> (a) Find the unit tangent and unit normal vectors T(t) and N(t). (b). Find the curvature k(t).

1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value...

1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value problem. yy'=e^x+x , y(0)=y_0 y_0 is a nonzero constant.

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Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x), x is in R. c) ut+ux=-tu, x is in R, t>0; u(x,0)=f(x), x is in R d)2ut+ux = -2u, x,t in R, t>0; u(x,t)=f(x,t) on the straight line x = t, where f is a given function.

Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2...

Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2 if t>=3 }

1. If T2 for gray matter is 100 msec at 1.5 T, it’s value for 3...

1. If T2 for gray matter is 100 msec at 1.5 T, it’s value for 3 T is most likely: a) 50 b) 70 c) 100 d) 140 e) 200 2.If transverse magnetization is Mxy the free induction decay signal is proportional to: a) (Mxy)-1 b) (Mxy)-0.5 c) (Mxy)0.5 d) (Mxy)1 e) Independent of Mxy

The curve C is given by the parameterization ⃗r(t) = <−t , 1 − t^2> for...

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