Civil Engineering Archive: Questions from December 07, 2023
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Solve the linear IVP: \( x \frac{d y}{d x}+y=\sin x, y\left(\frac{\pi}{2}\right)=\frac{2}{\pi} \) \( y(x)=\frac{\cos x+1}{x} \) \( y(x)=\frac{2-\sin x}{x} \) \( y(x)=\frac{1-\cos x}{x} \)1 answer -
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Solve the Cauchy-Euler IVP: \( x^{2} y^{\prime \prime}+x y^{\prime}+y=0, y(1)=1, y^{\prime}(1)=2 \) \[ \begin{array}{l} y(x)=x+x \ln x \\ y(x)=\cos (\ln x)+2 \sin (\ln x) \\ y(x)=\frac{1}{3 \sqrt{x}}\1 answer -
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