Question

This is a differential equations course, please answer all the questions.

Find the general solution.

2 11. :'(t) -3) r(t) 12. z"(t) = -1) =(4) 13. z'(t) = -3) =(0) 14. z'(t) = (-; -1)=(0) 2) -2 r(t) 5 10 15. z'(t) = 2 1 3 2 16. x'(t) = 0 2 1 -1 -2 - 1 -1 0 0 (t)

Answer 1

con [8] [:)] dx, = 28,5x2 - at exp AP = 1, -222 - differentiate on wort t atp 2dx dt - 5 dx2 dt 11 2dxi dt (2x2-1x)st 27P ixp2 = AP +10x2 АР 11Р = zda -5x + 10 (2x,- S dt = 2d2 -5x, +4x, -2 da, dt² AP AP ix -5x, +48 dez dx, tx=0 dt2

let D=m m²+1=0 m=ti 12,(t) = C, cost + C₂ sint differentiating q r 1 writt dt dt - 2dX2 dt X2 .(2x, -5%)-2022 dt2 dt 2 (de 1 + 2/2) – 52₂ - 2 dag dt2 dt 11 dt2 2 dx2 + 4x₂ -52₂ - zdx₂ dt 11 -I2 dt² +22=0 dt² (D²+1) 22=0 ; D = 1

let D=m m²+1=0 m=ti X(t) = Cy cost + Cg sont XCH= G cost & + C₂ sint 424) cost & la Sint Xit) cost +C₂ Snit