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Problem Let y = y ( x ) y=y(x) y = y ( x ) d y d x − ∣ A ∣ = 0 , for all x > 0 , where A = \frac{dy}{dx} - |A| = 0, \text{ for all } x > 0, \text{ where } A = d x d y − ∣ A ∣ = 0 , for all x > 0 , where A = [ y sin x 1 0 − 1 1 2 0 1 x ] \begin{bmatrix}
y & \sin x & 1 \\
0 & -1 & 1 \\
2 & 0 & \frac{1}{x}
\end{bmatrix} y 0 2 sin x − 1 0 1 1 x 1 y ( π ) = π + 2 y(\pi) = \pi + 2 y ( π ) = π + 2 y ( π 2 ) y\left(\frac{\pi}{2}\right) y ( 2 π ) π 2 + 4 π \frac{\pi}{2} + \frac{4}{\pi} 2 π + π 4 π 2 − 1 π \frac{\pi}{2} - \frac{1}{\pi} 2 π − π 1 3 π 2 − 1 π \frac{3\pi}{2} - \frac{1}{\pi} 2 3 π − π 1 π 2 − 4 π \frac{\pi}{2} - \frac{4}{\pi} 2 π − π 4 Browse the problem library