apply-eulers-method-with-x025delta-x025-to-approximate-y1y1-for-the-ivp-yxsinyyp

Question

Apply Euler's method with Δx=0.25\Delta x=0.25 to approximate y(1)y(1) for the IVP y′=xsin⁡$$yy^{\prime}=x$$\sin{y}, y(0)=π6y(0)=\frac{\pi}{6}. Round Euler's approximation to 44 decimal places. Also, determine the exact value of y(1)y(1).

Accepted Answer

y(1)≈0.7298y(1)\approx{0.7298} y(1)=2tan⁡−1(etan⁡π12)y(1)=2\$$tan^{-1}$$\left(\sqrt{e}	an{\frac{\pi}{12}}ight)

Answer

y(1)≈0.7298y(1)\approx{0.7298} y(1)=tan⁡−1(2etan⁡π6)y(1)=\$$tan^{-1}$$\left(\sqrt{2e}	an{\frac{\pi}{6}}ight)

Answer

y(1)≈0.8137y(1)\approx0.8137 y(1)=tan⁡−1(2etan⁡π6)y(1)=\$$tan^{-1}$$\left(\sqrt{2e}	an{\frac{\pi}{6}}ight)

Answer

y(1)≈0.8137y(1)\approx0.8137 y(1)=2tan⁡−1(etan⁡π12)y(1)=2\$$tan^{-1}$$\left(\sqrt{e}	an{\frac{\pi}{12}}ight)

Apply Euler's method with Δx=0.25\(\Delta\) x=0.25 to approximate y(1)y(1) for the IVP y′=xsinyy^{\(\prime\)}=x\(\sin{y}\), y(0)=π6y(0)=\(\frac{\pi}{6}\). Round Euler's approximation to 44 decimal places. Also, determine the exact value of y(1)y(1).

Apply Euler's method with $triangle x equals 0.25$ to approximate $y of 1$ for the IVP $y^{'} = x \sin y$ , $y (0) = \frac{π}{6}$ . Round Euler's approximation to $4$ decimal places. Also, determine the exact value of $y of 1$ .