Algebra problem. HELP!

Veröffentlicht von: PriyanshJ

I’m a civil engineering student and I have some algebra tasks to solve for my homework. I’m stuck on one of the problems! Can anyone help solve it? It’s d2y/dx2 − (coth x) dy/dx + (4 sinh^2 x)y = 0 Thank you in advance!

15.12.2020 2 Antworten

LoraT kommentierte am 15.12.2020

Hi, Priyansh! I’m not sure if I solved it correctly, but I think y = sinh x / 4 coth^3 But I’m an IT student and we don’t solve such complicated algebra problems, so I might be wrong.

TomasJ kommentierte am 15.12.2020

I have your solution: If t = cosh x, then dy/dt = (dx/dt) (dy/dx) = (1/ sinh x)(dy/dx). Then d2y/dt2 = (1/ sinh x) d dx ((1/ sinh x) dy dx ) = (1/ sinh2 x)d2y/dx2 − (cosh x/ sinh3 x)dy/dx ⇒ (sinh2 x)d2y/dt2 = d2y/dx2 − (coth x) dy/dx. Therefore the ode becomes sinh2 x d2y/dt2 + 4 sinh2 x y = 0 ⇒ d2y/dt2 + 4y = 0 ⇒ y = A cos 2t+B sin 2t. In terms of x, the solution is thus y = A cos(2 cosh x) + B sin(2 cosh x)