For an equation x" +x = 0 a) Draw a tangent vector to a solution (x(1), x' (1)) in the phase plane (x, x') at the point (1, 2)? b) Is the solution with initial data x(0) = 1 and x' (0) = 2 increasing or decreasing? Is it concave up or down?

Q: (c) 2ry'y-y²+²=0.

A: 2xy'y-y2+x2=0⇒2xyy'=y2-x2

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Q: y"'-3y"+2y'=t+et

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Q: Find the GS of y" - 2y' + y = 0

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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.