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Differential Equations
Answer the following and give complete solutions.
1. Find the constant a so that phi(x)=x(e^2x) is a solution to y'+ay-e^(2x)=0
2. Find the constant a so that e^xy + y = x-1 is an implicit solution to dy/dx = e^-xy +ay / e^-xy + x.
1. Find the constant a so that phi(x)=x(e^2x) is a solution to y'+ay-e^(2x)=0
2. Find the constant a so that e^xy + y = x-1 is an implicit solution to dy/dx = e^-xy +ay / e^-xy + x.
Differential Equations
Find a general solution for the differential equation
(D^2 - 3D +2) = (e^2x)/(1+e^2x)
(D^2 - 3D +2) = (e^2x)/(1+e^2x)
Differential Equations
Charles' law states that, for an ideal gas at a constant pressure, — = k, where V (liters), T (degrees Kelvin) and k is a constant (lit/°K). What does this model tell us?
Differential Equations
Solve the initial value problem "2f''(t)-3f'(t)+f(t)=te^t, f(0)=1,f'(0)=\\frac{3}{2}"
Using the point transformation [y = exp(ψ)], transform the equation (Eହ
) into a first
order non-linear O.D.E with independent variable x and dependent variable w, whereby w ≔ ψ
ᇱ
.
Afterwards, use the second point transformation ቂw =
ିଶఉᇲ(௫)
ఉ
ቃ to change this first order O.D.E to a
second order, linear and homogeneous O.D.E with independent variable x and dependent variable β .
Differential Equations
Solve the following initial value problem d^2 y/dx^2 +dy/dx -2y =-6 sin 2x -18 cos 2x , y(0) = 2, y'(0) = 2
Differential Equations
Solve the differential equation dy/dx +[x/1-x^2]y= x√y. y(0) =1
Differential Equations
Solve the initial value problem
y"(t)+ 2y'(t)+y(t)=3e^(-t) ; y'(0)=2 y(0)=4
y"(t)+ 2y'(t)+y(t)=3e^(-t) ; y'(0)=2 y(0)=4
Differential Equations
Consider the periodic function G(t)=e^t , 0≤ t < c, c a parameter.
G(t+c)=G(t).
Sketch the graph of G(t) and obtain its laplace form
G(t+c)=G(t).
Sketch the graph of G(t) and obtain its laplace form
Differential Equations
Find the general solution. If an initial condition is given, find also the corresponding particular solution and graph or sketch it. (Show the details of your work.yr y sin x ecos x, y(0) 2.5
Differential Equations
simple series circuit inductor 1 henry capacitor of 10 power minus 6 Faradas and a resistor of 1000 ohms . the initial charge on a capacitor is zero if a 12 volt battery is connected to the circuit and the circuit is closed at t = 0 find the charge on the capacitor 1 second later and the steady state charge
