Differential Equations Answers

6 Solve
(x3+y3)dx−3xy2dy=0
x5−2y3=Cx
x3−2y3=Cx
x3−3y3=Cx
x3−2y2=Cx

7 Solve
(1+2exy)dx+2exy(1−xy)dy=0
5x+2yexy=C
x+2ye2xy=C
x+2yexy=C
5x+3yexy=C

8 Solve
y(xy+1)dx+x(1+xy+x2y2)dy=0
2x2y2lny−2xy−1=Cx2y2
3x2y2lny−2xy−3=Cx2y2
2x2y2lny−xy=Cx2y2
2x3y2lny−2xy−1=Cx2y5

9 Solve
xdy−ydx−x2−y2−−−−−−√dx=0
Cx=2earcsinyx
Cx=earcsinyx
Cx=earcsin2y3x
Cx=earccosyx

10 The population of student P at NOUN increases at a rate proportional to the population and to the addition of 150,250 and the population divided by 3, the differential equation of this statement is
dPdT=3kP(150,250+P)4
dPdT=2kP(150,250+P)3
5dPdT=kP(150,250+P)3
dPdT=kP(150,250+P)3

6 The solution to the differential equation
(4+t2)dydt+2ty=4t
is
y=4t24+t2+c6+t2
y=2t34+t3+c4+t2
y=2t27+t2
y=2t24+t2+c4+t2
7 Find the general solution of the differential equation
dydx−2y=4−x
y=−12+23x+ce2x
y=−74+12x+ce2x
y=−74+22x+ce3x
y=−ln74+12x+celnx
8 Solve the initial value problem
xdydx+2y=4x2
,
y(1)=2
y=x2+1x2,x>0
y=3x2+1x2,x>0
y=x−2+1x2,x>0
y=x3+13x2,x>0

9 Solve for
dydx+y=5sin2x
y=ce2x−sin2x−2cos3x
y=ce−x+tan2x−2cos2x
y=ce−x+sin2x+3cos2x
y=ce−x+sin2x−2cos2x

10 Given the differential equation
dydx+(1x)y=3cos2x,x>0
the solution is __
y=cx+3cos2x4x+3sin22
y=cx+3cos2x4x
y=cx+3sin22
y=c2x+3cosx4x+3sin62

1. The differential equation
d2ydx2+(dydt)3=x2
is of order
3
2
1
0
2. 2 Any solution which is obtained from the general solution by giving particular values to the arbitrary constants is called ?
singular solution
definite solution
indefinite solution
Particular solution
3. If in an ordinary or partial differential equation, the dependent variables and its derivatives occur to degree one only, and not as higher powers or products, the equation is said to be
linear
singular
singleton
non linear
4. The _____ of a differential equation is the highest exponent of the highest order derivative appearing in it after the equation has been expressed in the form free from radicals and any fractional power of the derivatives or negative power.
order
total
power
degree
5. Which of the following represent the solution of the differential equation
d2ydx2+4y=0
5tan2x+5cos2x
5sin2x+4cos2x
5sin2x−3cos2x
5sin22x−3cos2x

suppose f(x,y) =x^3y^2 - sin^2xcos2y, what is df/dy?

6. Determine whether the following PDEs can be reduced to a set of two ODEs by the method
of separation of variables.

i) d^2 u / dx^2 + d^2 u / dy^2 = x

ii) x d^2 u / dx^2 + t du/dt = 0

1. a) Solve the following ordinary differential equations:

i) 1/x sin ydx + [(ln x)(cos y) + y)] dy = 0

ii) d^2 y / dx^2 + dy/dx - 12y = 4e^2x

b) Solve the initial value problem:

d^2 y / dx^2 + 2(dy/dx) + 2y=0, y(0)=2, y'(0)=1

please help me this question
http://i1376.photobucket.com/albums/ah26/john1x96/ex2_zpskjngf9zo.png

dy/dx = - (4+xy/x^2) + y^2 , find a solution to the ordinary differential equation in the form y1= ax^-1

: You place a cup of 210°F coffee on a table in a room that is 68°F, and 10 minutes later, it is 200°F . Approximately how long will it be before the coffee is 180°F? Use Newton's law of cooling: 180°F

A: 1 hour
B: 15 minutes
C: 35 minutes
D: 45 minutes

: A body was found at 6 a.m. Outdoors on a day when the temperature was 50°F . The medical examiner found the temperature of the body to be 66°F . What was the approximate time of death? Use newtons law of cooling, with k= 0.1947

T(t) = TA + (To – TA)e^-kt

A: 5 a.m.
B: 3 a.m.
C: 2 a.m.
D: Midnight (12 a.m.)

Find the differential equation of the family of curves y e (Acos x Bsin x) x = + where A and
B are arbitrary constants and hence solve the equation.