7. Jlgul * The first three non zero terms in a power series expansion of the solution for IVP y" -xy' -y = 0 with y(0) = 0, y' (0) = 1 are given by : %3D %3D O 1+x² + x 3. O x + 8 3! 8 .5 O 1+x+ ÷x³ 4.

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A: Given below the detailed solution.

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Q: x(х — 2)у" + 2(х — 1)у' — 2у %3D0 |

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.