Question

Question 9: Find the solution of the following initial- value problem, d x x² + xt subject to the initial condition dt 12 X = 1 at t = 1

Answer 1

aztat = here the giren Doe is; dx "x(1)=1 ta -) a2 - U) da at t t2 &t eq" (I) is the Bernoulli Dię of the form dx + pa=XQ ;- where pe o are the functions of 't do following the Algorithm Algorithm to solve Bernoulli's D.E. Dividing both sides of equation (1) by x da 22 'We get I . t2 xt x² at = du こ How het Tu 20 나 1 xdx x²dt Value in Abowe eg" we get (2) substituting du at + y = t t2 eq (2) is the linear D.E. so on dolering this I of = e logt こ女 dt dt t = e = e