Question

(5/10) find an implicit expression of all solutions y of the differential equation above, in the form \psi(t,y) = c, where c collects all constant terms, and \psi satisfies the

Answer 1

solution:

Consider the differential equation,

7ty + (1+t2)1/2y1 = 0

Rewrite the DE as,

(1+t2)1/2dy = - 7ty

dy/y = -7t/√1+t2 dt

in y = -7(1+t2) + c

y = ce-7(1+t2)

given,

y(0) = 1 => ce-7 = -1 => c = e7

ᴪ (t,y) = y -ce ᴪ(0,1)(1+t2)