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

Answer rating: 100% (QA)

a To solve the differential equation dydx x2y2x24y24 we can first separate the variables as dyy24 x24y24dx Then we can integrate both sides with respect to their respective variables to get 12 arctany... View the full answer