Questions - Differential Equations
Questions/Answers
Differential equations.
Anonymous has left a new comment on your post "Questions - Continuous
Compounding":
Can someone help me with the question below? Seems long, but they are
straightforward answers. Question) Classify the following equations -
linear, nonlinear, seperable, exact, homogeneous, or one that requires an
integrating factors as follows: . If an integrating factor is required,
specifiy it, BUT DO NOT SUBMIT SOLUTIONS TO ANY OF THE EQUATIONS BELOW.
Differential equations.
Anonymous has left a new comment on your post "Questions - Continuous
Compounding":
Can someone help me with the question below? Seems long, but they are
straightforward answers. Question) Classify the following equations -
linear, nonlinear, seperable, exact, homogeneous, or one that requires an
integrating factors as follows: . If an integrating factor is required,
specifiy it, BUT DO NOT SUBMIT SOLUTIONS TO ANY OF THE EQUATIONS BELOW.
YOU GAVE 20 PROBLEMS !!!.I AM GIVING THE METHODS TO FOLLOW WITH ONE
EXAMPLE EACH. YOU MAY PROCEED ACCORDINGLY AND TRY.
LEGEND:- Y' = DY/DX..Y"=D^2Y/DX^2 ETC..
L..LINEAR...NL..NON LINEAR...
S...VARIABLE SEPERABLE
H...HOMOGENEOUS..
NH..NON HOMOGENEOUS
E....EXACT....NE.....NOT EXACT
IF...INTEGRATING FACTOR
LINEAR: ALL THE DERIVATIVES SHALL BE IN FIRST DEGREE.
EX. 5Y""+4Y"' +2Y" +Y'=5X
NONLINEAR:ONE OR MORE DERIVATIVES WILL BE OF DEGREE 2 OR MORE
Y'^2+Y=5X
SEPERABLE: ALL X TERMS CAN BE SEPERATED OUT FROM ALL Y TERMS AND PUT
ON EITHER SIDE OF =
EX. (Y^2+Y+1)DY=(X^2+1)DX
HOMOGENEOUS:WHEN Y = VX IS PUT IN THE EQN.ALL 'X' TERMS CANCEL OUT
LEAVING ONLY V AND Y
EX. DY/DX = (3X+4Y)/(2X+Y)...PUT Y=VX TO GET.....DY/DX =
X(3+4V)/X(2+V)=(3+4V)/(2+V)
EXACT:THE EQUATION CAN BE PUT IN THE FORM OF
DERIVATIVE OF F(X) = CONSTANT ,THEN IT IS CALLED EXACT.THE TEST FOR
EXACT EQN.IS IF......
MDX+NDY=0
THEN
DOM/DOY = DON/DOX..WHERE DOM/DOY
REPRESENTS PARTIAL DERIVATIVE OF M WRT X.
EX. XDY+YDX = C
LHS = D(XY)
INTEGRATING FACTOR:IF AN EQUATION IS NOT EXACT BUT CAN BE MADE INTO AN
EXACT EQN.BY MULTIPLYING WITH SOME FUNCTION OF X AND Y THEN THAT
FUNCTION IS CALLED 'INTEGRATING FACTOR'
EX. YDX-XDY = 0 IS NOT EXACT SINCE
DOM/DOY=1 AND DON/DOX = -1
BUT THIS CAN BE MADE BY MULTIPLICATION WITH 1/Y^2
(YDX-XDY)/Y^2 = D(X/Y)
---------------------------------------------------
(a) dy/dx = (x^3 -2y) / x
EXAMPLE EACH. YOU MAY PROCEED ACCORDINGLY AND TRY.
LEGEND:- Y' = DY/DX..Y"=D^2Y/DX^2 ETC..
L..LINEAR...NL..NON LINEAR...
S...VARIABLE SEPERABLE
H...HOMOGENEOUS..
NH..NON HOMOGENEOUS
E....EXACT....NE.....NOT EXACT
IF...INTEGRATING FACTOR
LINEAR: ALL THE DERIVATIVES SHALL BE IN FIRST DEGREE.
EX. 5Y""+4Y"' +2Y" +Y'=5X
NONLINEAR:ONE OR MORE DERIVATIVES WILL BE OF DEGREE 2 OR MORE
Y'^2+Y=5X
SEPERABLE: ALL X TERMS CAN BE SEPERATED OUT FROM ALL Y TERMS AND PUT
ON EITHER SIDE OF =
EX. (Y^2+Y+1)DY=(X^2+1)DX
HOMOGENEOUS:WHEN Y = VX IS PUT IN THE EQN.ALL 'X' TERMS CANCEL OUT
LEAVING ONLY V AND Y
EX. DY/DX = (3X+4Y)/(2X+Y)...PUT Y=VX TO GET.....DY/DX =
X(3+4V)/X(2+V)=(3+4V)/(2+V)
EXACT:THE EQUATION CAN BE PUT IN THE FORM OF
DERIVATIVE OF F(X) = CONSTANT ,THEN IT IS CALLED EXACT.THE TEST FOR
EXACT EQN.IS IF......
MDX+NDY=0
THEN
DOM/DOY = DON/DOX..WHERE DOM/DOY
REPRESENTS PARTIAL DERIVATIVE OF M WRT X.
EX. XDY+YDX = C
LHS = D(XY)
INTEGRATING FACTOR:IF AN EQUATION IS NOT EXACT BUT CAN BE MADE INTO AN
EXACT EQN.BY MULTIPLYING WITH SOME FUNCTION OF X AND Y THEN THAT
FUNCTION IS CALLED 'INTEGRATING FACTOR'
EX. YDX-XDY = 0 IS NOT EXACT SINCE
DOM/DOY=1 AND DON/DOX = -1
BUT THIS CAN BE MADE BY MULTIPLICATION WITH 1/Y^2
(YDX-XDY)/Y^2 = D(X/Y)
---------------------------------------------------
(a) dy/dx = (x^3 -2y) / x
L.....NH.....NE .....IF=X
(b) (x + y)dx - (x -y)dy = 0
L.....H.......PUT Y=VX AND IT BECOMES S
(c) dy/dx = (2x + y)/ (3+ 3y^2 - x)
L.....NH......E
(d) (x + e^y)dy - dx = 0
L......NE.........IF = E^(-Y)
posted by mathsmanagementcommonsense at 6:25 AM
2 Comments:
Can someone help me with this?
For a second order differential equation of the form y" = f(x,y'), the substitutions v = y', v' = y" lead to a first order differential equations of the form v' = f(x,v). Provided that this is differential equation for v can be solved, y can be obtained by integrating
dy/dx = v(x)
Notice that one arbitary constant is introduced in solving the differential equation for v and that another is introduced when integrating v(x) to obtain y. Solve the following differential equation
x^2y" + 2xy' - 1 = 0
9:26 AM
How do you do this?
Divide x+3 into 2x^3+7x^2+x+3. Give the remainder and tell whether x+3 is a factor of 2x^3+x+3.
In the problem above, for what value of x does 2x^3+7x^2+x+3 equal 9? Find the solution w/o using direct substitution if you can, and explain your answer in terms of the remainder theorem.
Thank you
11:37 AM
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