MTH382
Question: State the order and whether they are linear or non linear the following D.E \\((1-x) y^{\’\’}-4xy^{\’}+5y=\\( cos x\\)
Answer: second order linear
Question: Determine the order of the following differential equation \\( y^{\’}y^{\’\’}=t^3\\)
Answer: order 2
Question: Which of the following function y(t) is a solution of \\( y^{\’}=3y+12\\) on the given interval I
Answer: \\( y(t)=ce^{3t}-4\\)
Question: Consider the differential equation\\(( y^{\’}=y-t\\) determine which of the following functions defined on the interval \\(-\\infty, \\infty\\) are solutions
Answer: A and B
Question: The standard form of the differential equation in question \\( y^{\’}y^{\’\’}=t^3\\) is
Answer: \\( y^{\’\’}=\\(frac{t^3}{y^{\’}}\\)
Question: A differential equation that describes some physical process is often called a…
Answer: Mathematical model
Question: A solution of a differential that is identically zero on an interval I is said to be a..:
Answer: trivial solution
Question: State the order and whether they are linear or non linear the following D.E \\(t^5 y^(4)-t^3y^{\’\’}+6y=0\\)
Answer: fourth order linear
Question: Solve \\( y^{\’}=e^{2t}-1\\)
Answer: \\( y(t)=\\(frac{e^{2t}}{2}-t+c\\)
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