Question

(xlnx)y'+y= 3x^3 x>0

Answer #1

solve ivp: (y+6x^2)dx + (xlnx-2xy)dy = 0, y(1)=2, x>0

solve for x(t) and y(t):
x'=-3x+2y;
y'=-3x+4y
x(0)=0,y(0)=2

Solve the initial value problem
x′=−3x−y,
y′= 13x+y,
x(0) = 0,
y(0) = 1.

solve the following systems
x'=3x-y+2 , x(0)=1
y'=-4y , y(0) =2

dx
dt
= y − 1
dy
dt
= −3x + 2y
x(0) = 0, y(0) = 0

3. Consider the equation (3x^2y + y^2)dx + (x^3 + 2xy + 5)dy =
0. (a) Verify this is an exact equation
(b) Solve the equation

Let X and Y have a joint density function given by f(x; y) = 3x;
0 <= y <= x <= 1
(a) Find P(X<2Y).
(b) Find cov(X,Y).
(c) Find P(X < 1/2 |Y = 1/3).
(d) Find P(X = 1/2|Y = 1/3).
(e) Find P(X > 1/2|Y > 1/3).
(f) Find the conditional expectation E(X|Y = y).

find y' for the function
1. (y-2)^7=3x^2+2x-2
2. 3y^3+2x^3=3
3.(4y^2+3)^4+3x^5-5=0
4. 4x^2+3x^2y^2-y^3=3x

8) Suppose a consumer’s utility function is defined by
u(x,y)=3x+y for every x≥0 and y≥0 and
the consumer’s initial endowment of wealth is w=100. Graphically
depict the income and
substitution effects for this consumer if initially Px=1 =Py and
then the price of commodity x
decreases to Px=1/2.

(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that H(x,
y) ≥ 0 for all (x, y). Hint: find the minimum value of H.
(4) Let f(x, y) = (y − x^2 ) (y − 2x^2 ). Show that the origin
is a critical point for f which is a saddle point, even though on
any line through the origin, f has a local minimum at (0, 0)

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