find the general solution of the given differential
equation.
1. y'' + y = tan t, 0 < t < π/2
2. y'' + 4y' + 4y = t-2 e-2t , t >
0
find the solution of the given initial value problem.
3. y'' + y' − 2y = 2t, y(0) = 0, y'(0) = 1
An individual utility function is given by U(x,y) =
x·y1/2. This individual demand equation for x is a
factor a of I/px: x* = a (I/px). In this
specific case, factor a is equal to ______. (NOTE: Write your
answer in number format, with 2 decimal places of precision level;
do not write your answer as a fraction. Add a leading zero and
trailing zeros when needed.)
a)
Let y be the solution of the equation y ′ =
(y/x)+1+(y^2/x^2) satisfying the condition y ( 1 ) = 0.
Find the value of the function f ( x ) = (y ( x ))/x
at x = e^(pi/4) .
b)
Let y be the solution of the equation y ′ = (y/x) −
(y^2/x^2) satisfying the condition y ( 1 ) = 1. Find the
value of the function f ( x ) = x/(y(x))
at x = e .
c)
Let y be the solution...