Solve the following problem: dh 10.3 + 0.002 (52.1h + 10.3h. - 1.17(1 – sin 3t) = 0.0308, with h(0)-4 Where h denotes the liquid level (measured in meters) and t denotes the time (minutes). Find the liquid level at t-4 minutes using Euler's and Heun method. Assume step size of 1 minute. Plot your result. (Use caleulator in radians) Question 2 (Example 8.2) Use (a) Euler's and (b) the Heun method to solve the following set of differential equations, assuming that x = 0, y1 = 4, y2 = 6. Find the value of y, and y2 at x-2 with step size of 0.5. dy = -0.5y1 dy = 4-0.3yz - 0.1y1

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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.