Advanced Math Archive: Questions from December 18, 2022
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2 answers
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Solve \( F_{\mathrm{yy}}+3 F_{\mathrm{xy}}+2 F_{\mathrm{xx}}=-3 x, F(x, 0)=3 x, \partial_{y} F(x, 0)=0 \) \[ F(x, y)= \]2 answers -
\( \left[3\left(\cos 120^{\circ}+i \sin 120^{\circ}\right)\right]\left[4\left(\cos 270^{\circ}+i \sin 270^{\circ}\right)\right] \)2 answers -
Solve \( u_{x}(y+2 u)+u_{y} y=2 x-y, \quad u(x, 1)=x+1 \). i.e. find an explicit solution for \( u=u(x, y) \) subject to \( u=x+1 \) when \( y=1 \). \( u(x, y)= \)2 answers -
2. Solve the following differential equations. (a) \( y^{\prime}=\frac{e^{y}}{x(x+2)} \), (b) \( y^{\prime}=y^{4} \frac{\cos x}{\sin x+2} \), (c) \( y^{\prime}=3 y+x \), (d) \( y^{\prime}-\frac{4 y}{x2 answers -
2 answers
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2 answers
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2 answers
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(1 point) Solve the initial value problem \[ y^{\prime \prime}+1 x y^{\prime}-4 y=0, y(0)=9, y^{\prime}(0)=0 \] \[ y= \]2 answers