Question

1. [20 pts.] Solve (t +1)e^t + (ye^y −te^t )y' 0 = 0

Answer #1

y"-3y''''+2y= te^2t, y(0)=1, y''(0)=4
solve

Solve the differential equation y' = 1 +te^(-y)
using substitution u= e^(y)

y'+y cos t = y^2 te^ sint
Solve the equation

solve using the laplace transform y''-2y'+y=e^-t , y(0)=0 ,
y'(0)=1

y^''-y^'-2y= e^t , y(0)=0 and y^'(0)=1
Solve by using laplace transform

Solve y'' + 4y = delta(t-7) + delta(t-20); y(0)=y'(0)=1. sketch a
graph 0<=t<=25

Solve the following equation using integrating factor.
y dx + (2x − ye^y) dy = 0

Solve the initial value problem
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

Solve the IVP y¨ − 5 y˙ + 4y = e^t , y(0) = 3, y˙(0) = 1/3

1. Solve the following IVP's given the initial conditions:
a) y'(t) - 10(√t)y(t) =
e(20/3)(t^3/2) ; y(0) = 2
b) x' - 2x = (et)(cos(t)) ; x(0) = 5
c) dx/dt + (1/t)x = ln(t) ; x(1) = 1/2

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