Advanced Math Archive: Questions from November 17, 2022
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Find \( Y(5) \) \( y^{\prime \prime \prime}+4 y^{\prime \prime}+y^{\prime}-6 y=-12 \) \( y(0)=1 \quad \quad y^{\prime \prime}(0)=4 \quad y^{\prime \prime}(0)=-2 \)2 answers -
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9. The singular solution for the Clairaut equation \( y=x y^{\prime}+\left(y^{\prime}+5\right)^{3} \) is: (a) \( \left.y=\left(\frac{z}{3}-5\right)-(z)\right)^{3} \) (b) \( y=\left(\begin{array}{l}3 \2 answers -
\( \left.y^{\prime \prime}-4 y^{\prime}+4 y=e^{2 x}(1+x)+e^{2 x} \cos x-\sin x\right)+3 e^{3 x}+1+x \)2 answers -
1. Comente los tres diferentes casos que nos podemos encontrar al resolver una ecuación con valor absoluto. 2. Presente un ejemplo original resuelto de cada caso. 3. Comente con al menos 2 companeros0 answers -
Solve the following (non-homogeneous) IVP \[ \mathbf{y}^{\prime}=\left(\begin{array}{rr} 0 & 1 \\ -6 & 5 \end{array}\right) \mathbf{y}+\left(\begin{array}{r} 0 \\ 2 e^{x} \end{array}\right), \quad \ma2 answers -
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Verify the identity. \[ \begin{aligned} 6 \cos ^{2}(x)-3 &=3-6 \sin ^{2}(x) \\ 6 \cos ^{2}(x)-3 &=6(1-(\\ &=6-(\\ &=3-6 \sin ^{2}(x) \end{aligned} \] SALGTRIG4 7.1.067. 0/10 Submissions Used Verify th2 answers -
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A particular solution of \( y^{\prime \prime}-y^{\prime}-6 y=2 \sin (3 x) \) a. \( \frac{1}{2} \cos (3 x)-5 \sin (3 x) \) b. \( \frac{8}{13} \cos (3 x)-3 \sin (3 x) \) c. \( 4 \cos (3 x)-5 \sin (3 x)2 answers -
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Evaluate \( \iiint_{E}(x+y-3 z) d V \) where \( E=\left\{(x, y, z) \mid-7 \leq y \leq 0,0 \leq x \leq y, 02 answers -
Evaluate \( \iiint_{E}(x+y-3 z) d V \) where \( E=\left\{(x, y, z) \mid-7 \leq y \leq 0,0 \leq x \leq y, 02 answers -
2(a) Show that \[ x(\pi-x)=\frac{8}{\pi}\left(\frac{\sin x}{1^{3}}+\frac{\sin 3 x}{3^{3}}+\frac{\sin 5 x}{5^{3}}+\cdots \cdots\right) \text { for } 0 \leq x \leq \pi, \] using the appropriate half-ran2 answers -
7. Find \( \operatorname{Res}(f, 0) \) if \( f(z)=\frac{\mathrm{e}^{\mathrm{e}}}{\cos z-1} \). 8. Find \( \operatorname{Res}(f, 0) \) if \( f(z)=\frac{1}{z^{2} \sin z} \).2 answers