Question

2. Show that if p is differentiable and p(t) > 0, then the Wronskian W(t) of two solutions of [p(t)y'l' +q(t)y = 0 is W(t) = po where c is a constant.

Answer 1

* g"+ blog + 2 y = 0 Comparing * with gut alty' + b(48=0 we have. - [In b (t] till 2. Given differential equation is (bltby'}'+ et q (t) y 0 or, bctly" p'ltsy't + 2(+) y = 0 q(t). or, y "+ b(t) bct) alt) = By the Abel's formula we have -faces de W=kie =kie Infltol-ln (P(t). =k. é kie Inpito) in Yolt) sk.e b'(t) blt). and blt) = 21t). bl) it pt b'(t) dt to bit) to t. k.blto). I bit) G with = Where G = K.plto) is a Constanta blt)