Question

Now I have and ult=o= o. d 2 +2 I How can I get the eq (x-xo + I) ² - t² = 7 !

Integral equation

Answer 1

Giveni du = (1-4²) 12 ao and u (t=0) = 0 dt du - adt I using variable separable -u232 on equation of Integrating both sides du = ladt 2 - Now let U=Sino au=coso do then l du = ( coso do (1-42) 3/2 J (1-Six²0) 3/2 I du cosodo -sino 7 1-42)3/2 I (cop²0)/ =los? coso do s I do I du 312 = (secodo o = sec of - tano (see odo= tane] " : tano - Sino du I au ki ujitz = no JH-u bo @ and tanda singolare - sinzo = Jismo tanco - Since-ul from u = faedt u ao fat

: Sidt=t and c= Julegration 7 constant put in abo we equation u = got tc Ft Now at tao thao 0 = ao(o)tc To=c] put in u = got u = got (1-4² sauaring both sides u 2 = a 2 +2 (1-4²) u² = 902t² - azt²u² u²+ a2t² u² = 92+2 U2 (1 + a² + ²) = a0²t2 u 2 = 90²t2 n u = 90²t² 1 +90242 ✓ Hazt² u = not Janez dx = at at dx - Ilta 2+2 dot at Ita 242 T velocity u-da7 att Integrating both Sides I = tart2 lat ta 242 dt 5

derivate both sides Now let 11790²t2 = ÞI des of ar at dt = dp 290²t dt = dp at = dp 2007 Thence I atet - r got db Ita²42 ar de Jp 203t J 2264JB = 240 solle de 172+1 Сая ntt T --- nt c-Integration Constant o Is - | Je to = t tast to not dt ath from 6 and 6 ao Intial postoran x = 1 1+1242 + c Now at t=0 2=X6 hence do = I J 1 +90 (02 + c

fut in to to Xo = a tc (16 2 2 = C = 1 51 +92 +2 + x - 720 ( - Xo +1 = 1/ +4 () savaring both sides 4x=x0+ 1) = 02 (1+90 € (X-Rat & ) ² = a b + as the (11-otto = a 2 + + I (X-tott ² - t ² = 1 1 2 A 12 lto = Hand hence Proved