A series solution around the point x,=0 of the differential equation defined by d?y dy dx -2x +y=0 dx2 is a sries written on the form 00 (v(x)=2a, - a+ ((n+2) (n+1)a + (1– 2n)a n+2 n=1 (y (x) =2a,-a+ 2( (n+2) (n+1) an+2+(1-2n) a,) x" n=2 y(x) =2a,-a+ 2((n+2) (n+1) an+2+ (1-2n) a,) x" n=0 y(x) =2a2-ao+ 2¸((n+2) (n+1) an+2+(1-2n) a,) x^-1 n=1

Q: (a) 2xy? + x²y' = y², y(1) = = -1 (а) Зу(2? — 1) + (»3 + 8y — За) dy (b) 4x?3 dy гу* + 2 dæ (e) xy'…

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Q: a) dy dx xe ex²+ y(0)=1

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Q: transcribe the following text in digital format

A: In the question, it is asked to transcribe the given text in the screenshot to digital format.…

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.