Math  /  Calculus

QuestionChoose the correct answer : (5 points) 1) A particular solution for the differential equation y(4)+y(3)=2+4exy^{(4)}+y^{(3)}=2+4 e^{x} is (a) A+Bex\mathrm{A}+\mathrm{B} \mathrm{e}^{\mathrm{x}} (b) A+Bx+Cx2+Dex\mathrm{A}+\mathrm{Bx}+\mathrm{Cx}^{2}+\mathrm{D} \mathrm{e}^{\mathrm{x}} (c) Ax2+Bx2ex\mathrm{Ax}^{2}+\mathrm{Bx}^{2} \mathrm{e}^{\mathrm{x}} (d) Ax2+Bex\mathrm{Ax}^{2}+\mathrm{Be}^{\mathrm{x}} e)NOTA 2) The solution for the I.V.P sin(t)y+1t3y+ety=t3y(1)=0y(1)=1y(1)=1\sin (t) y^{\prime \prime \prime}+\frac{1}{t-3} y^{\prime \prime}+e^{t} y=t^{3} \quad y(1)=0 \quad y^{\prime}(1)=1 \quad y^{\prime \prime}(1)=-1 is guaranteed on a) (0,3)(0,3) b) (0,π)(0, \pi) c) (,3)(-\infty, 3) d) (,)(-\infty, \infty) 3) If a series solution is to be found for y4xy+4y=0,y(0)=2,y(0)=3y^{\prime \prime}-4 x y^{\prime}+4 y=0, y(0)=2, y^{\prime}(0)=3 then a2=\mathrm{a}_{2}= (a) -4 (b) 8 (c) -8 (d) 1 e)NOTA 4)Suppose the solution to the differential equation y+3y=0y^{\prime \prime}+3 y=0 is written as a power series y=n=0anxny=\sum_{n=0}^{\infty} a_{n} x^{n} What is the lower bound of the radius of convergence of this power series? a) 0 b)1 c)2 d) 3 e) \infty 5) The general solution for y+9y=0y^{\prime \prime \prime}+9 y^{\prime}=0 is : a) c1+c2cost+c3sintc_{1}+c_{2} \cos t+c_{3} \sin t b) c1+c2t+c3e9tc_{1}+c_{2} t+c_{3} e^{9 t} c) c1+c2e3t+c3e3tc_{1}+c_{2} e^{3 t}+c_{3} e^{-3 t} d) c1+c2e3t+c3te3tc_{1}+c_{2} e^{3 t}+c_{3} t e^{3 t} e)NOTA

Studdy Solution
1. (d)
2. (a)
3. (a)
4. (e)
5. (e)

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