Question

Can someone help me with this problem please?

1.4 Let u(x, y) = h(Vx2 + y2) be a solution of the minimal surface equation. (a) Show that h(r) satisfies the ODE rh" +h'(1 + (h')2) = 0. (b) What is the general solution to the equation of part (a)?

Answer 1

u (x,y) = n(Vx2442) isider the 2nd onder non linear PDE . (Hug) uxx - 24x My egy + (Hue) ayy = 0 Let 4(X,Y)=h(n), n= √22ty2 there there are the Now, Ux (x,y) = n(n) on SV 22ty2 2x an 2x 2 224 42 V x2fyL NOW, an 1x²f42 y21 Valt42 2x tyl ² tyz I xhof uxxe = te voren (tiens Wome n = noms en het voertuig t ning var en ny on väike de scris in the thing trijon — lays (4) = (Hem vor mine) Ways h"cm) em nos con ) + temo (o every one) =h"cms y - uCW xeyager I uy = f (ren) tye) K24 YL XY I 42 / V x²fyl / 61 x2 +42 12 22 KY xy n

122.42 Vad ty) nemmeno un ) + 16m) Valoyz .-Y27 (tyt ) ? axy = tem v tem +1cm) cena 24742 in eran ☺ putting all this value THE ХУ V24 NEW 14 XLt4 22442 W22 42 2/84 444 flalyly (1+6° ) (nu that and turn on are ) - en el centro ) (no tiene un ) * (i to write) Cinematon a yol ) = 0 >> All tu' cere un ) +(116(en => "(1) tú (internet )+( 12 le co >> Ws" (#) +673 ) - 0 s n" + x' (to) +Cup. To have to => rn" tń (1+(40)4) so 442 Proved