A.9.1: Section 9.1 Answers
- Page ID
- 43790
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2. \(y=2x^{2}-3x^{3}+\frac{1}{x}\)
3. \(y=2e^{x}+3e^{-x}-e^{2x}+e^{-3x}\)
4. \(y_{i}=\frac{(x-x_{0})^{i-1}}{(i-1)!},\quad 1\leq i\leq n\)
5.
b. \(y_{1}=-\frac{1}{2}x^{3}+x^{2}+\frac{1}{2x},\quad y_{2}=\frac{1}{3}x^{2}-\frac{1}{3x},\quad y_{3}=\frac{1}{4}x^{3}-\frac{1}{3}x^{2}+\frac{1}{12x}\)
c. \(y=k_{0}y_{1}+k_{1}y_{2}+k_{2}y_{3}\)
7. \(2e^{-x^{2}}\)
8. \(\sqrt{2}K\cos x\)
9.
a. \(W(x)=2e^{3x}\)
d. \(y=e^{x}(c_{1}+c_{2}x+c_{3}x^{2})\)
10.
- \(2\)
- \(-e^{3x}\)
- \(4\)
- \(4/x^{2}\)
- \(1\)
- \(2x\)
- \(2/x^{2}\)
- \(e^{x}(x^{2}-2x+2)\)
- \(-240/x^{5}\)
- \(6e^{2x}(2x-1)\)
- \(-128x\)
24.
- \(y'''=0\)
- \(xy'''-y''-xy'+y=0\)
- \((2x-3)y'''-2y''-(2x-5)y'=0\)
- \((x^{2}-2x+2)y'''-x^{2}y''+2xy'-2y=0\)
- \(x^{3}y'''+x^{2}y''-2xy'+2y=9\)
- \((3x-1)y'''-(12x-1)y''+9(x+1)y'-9y=0\)
- \(x^{4}y^{(4)}+5x^{3}y'''-3x^{2}y''-6xy'+6y=0\)
- \(x^{4}y^{(4)}+3x^{2}y'''-x^{2}y''+2xy'-2y=0\)
- \((2x-1)y^{(4)}-4xy'''+(5-2x)y''+4xy'-4y=0\)
- \(xy^{(4)}-y'''-4xy''+4y'=0\)