Question

b. ASSUME the Differential Equation: dx dt :-(W2)x. 1. SOLVE. That is, determine a function x = f(t) which satisfies the above. 2. CHECK. Show that your function to the above dif. eg. is, indeed, a solution.

Show all steps please.

Answer 1

Solution, I Given differential Equation dz را اترا ۔ can regras this equation as لے گیا ۔ I da - integrating both side (Assure w is a constant) ، ۔۔۔ Sata s i de ہوا ۔ OR CX = x = C е, loge at logge C (here is the philegration constant.) -63t = loge ca e ult -wit (ii) this is the required solution which is in the form x= f(t). To show that a solution of our differential equation, put 다 in given differential equation de - Cote wity e'x leuit) 2 . و اي = w} is, indud x= ē wat LHS dt х -w2 x حبه ۔ da at -w²x Hence proved