1 A differential equation is given along with the field or problem area in which
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Question
1 A differential equation is given along with the field or problem area in which it arises. Classify it as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear dy dx =C, where C is a constant (brachistochrone problem, calculus of variations) Classify the given differential equation. Choose the correct answer below. O O O partial differential equation nonlinear ordinary differential equation linear ordinary differential equation The order of the differential equation is (Type a whole number.) The independent and the dependent A differential equation is given along with the field or problem area in which it arises. Classify it as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables.the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear. d2 dx (Kidders equation, fiow of gases through a porous medium) Classify the given differential equation. Choose the correct answer below O O O nonlinear ordinary differential equation linear ordinary differential equation partial differential equation The order of the differential equation is Type a whole number.) The independent and the dependent | 3. (a) Show that y.x-6-0isan implot Dolufon to onthe interval (-00,6). xy.xy5 coax. 1 is an ipicit sout on to the diferential equation. ( xsin . cos xcosx) 1 (b) Show that on the interval (0, 2x) (a) To verfy the solution and the interval, convert y x-6 0 to ext functions). y(Use a comma to separate answers as needed) Find the derivativeys) of the axpicit solution(s). -D (Use a comma bo separate ar wers a8 needed.) When the explot solutor s) tor y isiare substated into--=-- the two sides of te e uason are oquMaert. Explan why the souton is limited to interval (-de,6). Coo so te oomoct answer bolow. A. Neither y norakare roalvaued for x>6,and y is undoined at x-6. OB. Neither y nor dy are realwauedforotanddyisundefined atxs6. O C. y is undefined for x26 OD. Neither y nor x are defned for x26 (b)To verify the solution and the iterval, convert-xy5 coax-1to explicit unctions). y(Use a comma to separate answars as needed) dy Find the denivativo(s) of the oxpicit solution(s) Use a comma to separato anowers as nooded.) When the explic selusons) fory are subatituted int the two sides of the equation are equivalent. Explain why the soluion interval does not include 0 or 2. Select all that apply A. da C. yís undefined at x . 0and x.21. is undefined atx.0and x.2n. yis undefined ty=0and y=2tExplanation / Answer
1. Since the differential equation contains total derivative term not partial derivative so the differential equation is ordinary differential equation.
Also power of highest order derivative is 2 so the differential equation is non linear.
It contains first order derivative term as the highest order derivative term so order of the differential equation is 1.
y is differentiated w.r.t. x so dependent variable is y and independent variable is x.
Pls post other questions separately.Thank you.
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