Use the modified Euler formula, y,+1 = y, + hf tn + ÷h, y, +¬hf (tn, Yn)|, with h = 0.05 to compute approximate values of (In, Yn) the solution of the given initial value problem at t = 0.1,0.2,0.3 and 0.4: y' = 3 +t - y, y(0) = 1. Make all calculations as accurately as possible and round your final answers to five decimal places. tn = nh Ул n = 2 0.1 i n = 4 0.2 i n = 6 0.3 n = 8 0.4 i

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Q: 4. Find the general solution: 2r (a) z'=

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Q: Find the derivative of the function. y = x2 ln x2

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Q: Solve the IVP: X' = AX, where -() xw - () 3 -3 1 A = 2 -1 0 1 -1 1 and 7 X(0) 4 3

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Q: The solution of the following IVP:y' = y³ x ex´ , v(0) = 1

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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.