Question

这个超越式方程能解出解析解吗?其中除x外都是常数

Answer 1

x=Ax0

y=arc sin [b/((b^2 +c^2)^(1/2))]

sin y = b/((b^2 +c^2)^(1/2))

cos y = c/((b^2 +c^2)^(1/2))

a=e^(-x) *(b sin x +c cos x)

=(b^2 +c^2)^(1/2)* e^(-x) *(sin y sin x + cos y cos x)

=(b^2 +c^2)^(1/2)* e^(-x) *cos(x+y)=a

e^(-x) *cos(x+y)=a /[(b^2 +c^2)^(1/2)]

small x,x=-y+arc cos {a /[(b^2 +c^2)^(1/2)]}

large x, a small, x+y=3.1416/2, x=3.1416/2 - y