Question

5. Find the solution of the differential equation = that satisfies y(0) = 1. dx 2yV1–22

Answer 1

Solution W dy du g (0) = 1 ayri-q? 7 2y dy = - 1 z du Integrating both sides, we get > a[edy --Store St (dz) + c 7 y2 = 122 Su dz to 7 y2 = 3 7y2 = 1 / 2 x (z 2) te Z 2 y ² 2 put z=1-12 > dz=-anda => dx = dz -zu z 3+1 nda- dz -2 te - +1 | 7 y2 = zit t y2 = V1 -2² te 0 Uning the initial condition y(o) = 1 In equation o, we get > 12 =vi-oto c=1-1-0 ly² = 1-2² is the required particulare solution.