Other Math Archive: Questions from November 26, 2022
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3. Solve (a) \( y^{\prime}-\frac{2}{x^{3}} y=0 \). (b) \( y^{\prime}+\frac{2}{x^{3}} y=0, y(2)=3 \). (c) \( y^{\prime}+\frac{2}{x^{3}} y=0, y(0)=3 \). (d) \( y^{\prime}+\frac{2}{x} y=\frac{\cos x}{x^{2 answers -
1. Solve (a) \( y^{\prime}+\tan (x) y=x \sin (2 x) \). (b) \( y^{\prime}-3 x^{2} y=-x^{2}, y(0)=1 \). 2. Solve \( y^{\prime}+\left(\frac{\ln ^{2} x}{\sin ^{2} x}\right) y=0, y(5)=0 \). 3. Solve (a) \(2 answers -
Determine whether \( f^{\prime}(0) \) exists. \[ f(x)=\left\{\begin{array}{ll} x \sin \frac{1}{x} & \text { if } x \neq 0 \\ 0 & \text { if } x=0 \end{array}\right. \]2 answers -
1 answer
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Prove the following
\( \left(a_{1} a_{2} \cdots a_{2^{n}}\right)^{1 / 2^{n}} \leq \frac{a_{1}+a_{2}+\cdots+a_{2^{n}}}{2^{n}}, n=1,2, \ldots \), y las \( a_{i} \) son números positivos.2 answers -
2. Use the Laplace transforms to solve the following initial value problems. a. \( y^{\prime}+5 y=e^{6 t}, y(0)=1 \). b. \( 6 y^{\prime}+12 y=39 \sin 3 t, y(0)=\frac{1}{2} \). c. \( y^{\prime \prime}+2 answers -
2 answers
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2 answers