whereupon, the solution to the initial-value problem become 2 cos 2t-2 sin 21 + 48 48 Supplementary Solve the following initial-value problems. 13.7.) y"-y' - 2y = e*; y(0) = 1, y'(0) = 2 %3D y" -y - 2y = e*; y(0) = 2, y'(0) = 1 13.8. %3D 13.9.) y"-y - 2y = 0; y(0) = 2, y'(0) = 1 13.10. y"-y-2y = e3*, y(1) = 2, y'(1) = 1 13.11. y"+y = x; y(1) = 0, y'(1) = 1 13.12. y"+ 4y = sin? 2x; y(T) = 0, y(T) = 0 %3D %3D 13.13. )y" + y=0; y(2) = 0, y'(2) = 0 %3D 13.14. y" = 12; y(1) = 0, y'(1) = 0, y"(1) = 0 %3D %3D 13.15. ÿ+2ÿ+2y = sin 2t + cos 2t; y(0) = 0, ý(0) = 1 %3D %3D

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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.