Q4. (a) State the second order Cauchy-Euler equation. Determine the different types of solutions of it depending over the nature of the roots of the characteristic equation. (b) Solve for general solution using the variation of parameter method x²y" – 2xy' + 2y = xFe* (c ) find the particular solution using y(1) = -1 and y'(1) = 2

Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: titution: 4 11 8 }]ÿ. y(0) = [¯²]. etermined coefficients: 12 -1 · [¹² −¹5]y+[e²].

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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.