# Ordinary Differential Equations

I am going to have a test tomorrow from 9.00 pm (Denmark time) and I will give it to you at 09.20 because I need to translate it. I need to have it done by 12.20 it will be 10 questions and for each question there are multiple choices and only one is correct you will have a-e and only one of the solutions is correct and you must know which one.  The math test will contain the following which you must know to be able to solve: handle separable differential equations  and linear ordinary   differential equations  Ordinary differential equations. Taylor’s formula.  Approximation of functions.  Numerical methods. Vector value functions.  Numerical methods.  I am going to give you some examples of what kind of questions it will be. (tomorrow I will write it by hand and it will be more clear) example: Separete xy’= y+ xy a)you can’t b)∫1/y dy= ∫(x+1)dx  c) ∫y dy= ∫(1+1/x)dx      d) ∫1/y dy= ∫(1+1/x)dx    e) none of the choices       Determine the homogeneous solution to y” +4y’+ 4y= x+ 1.  a) y(x)=e-2x(C1cos(2x)+C2sin(2x) b) y(x)=e-2x(C1+C2x) c) y(x)=C1-2x+ C2 e-x d)y(x)=C1e-2x +C2 e-4x e) none of the choices Determine the integrating factor y’-6y=e x a) you can’t b) IF=e6x c) IF=e3x2 d) IF=ex e) none of the choices  Solve the differential equation xy’=y+xy  a)y(x)=C1+ 1/2×2 b) y(x)=C1x3 c) y(x)=xln(y)+C1 d(y(x)=C1x e) none of the choices

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