Solve each differential equation.

a) dy/dx= x^2y^2−x^2+4y2−4

b) (x-1)dy/dx - xy=e^4x

c) (7x-3y)dx+(6y-3x)dy=0

Solve the following initial value problem

1) (3x^2 + y-2)dx +(x+2y)dy=0 y(2)=3

2)show that 5xy^2 + sin(y)= sin(x^2 +1) is an implicite solution to the differential equation: dy/dx=2xcos(x^2+1)-5y^2/10xy+cos(y)

3) find value for k for which y= e^kx is a solution of the differential equation y"-11y'+28y=0

4)A tank contains 480 gallons of water in which 60 lbs of salt are dissolved. A saline solution containing 0.5 lbs of salt per gallon is pumped into the tank at the rate of 2 gallons per minute. The well-mixed solution is pumped out at the rate of 4 gallons per minute. Set up an initial value problem which can be solved for the amount A of salt in the tank at time t

5)

Consider the following differential equation:

sin(x) d^3y/dx^3-x^2 dy/dx+y= lnx

(a) Is the equation linear ornonlinear?

(b) Is it a partial or ordinary differential equation?

(c) What is the order of the equation?

6) Verify that

y= x^2 ln(x) is a solution of

x^2 y"' + 2xy"- 3y'+ (1/x) y= 5x- xln(x)

on the interval (0, inf)

8)

Determine if the following differential equation is homogeneous or not.

3x^2 y dx + (x^2 + y^2)dy=0