Question

Matlab能解答带参数的微分方程吗？解答出来的解里面要带有方程中的参数的

Answer 1

用dsolve
dsolve('Dx = -a*x')

ans = C1/exp(a*t)

追问

d(T0-Tx)/dt=Ud-h(T0-Tx)-a(T0^4-Tx^4),求解Tx，这个方程也能用 dsolve解吗？

追答

替换一下 y=T0-Tx--->Tx=T0-y
dy/dt=Ud-hy-a(T0^4-(T0-y)^4)

dsolve('Dy=Ud-h*y-a*(T0^4-(T0-y)^4)','t')

ans =

solve(t - C3 + sum(c*log(4*y - 4*T0 - 16*Ud*c + 4*T0*c*h + 12*c*h*y + 16*T0^4*a*c), c in RootOf(768*T0*Ud^2*a*d^4*h - 1536*T0^5*Ud*a^2*d^4*h - 768*T0^2*Ud*a*d^4*h^2 + 768*T0^9*a^3*d^4*h + 256*T0^3*a*d^4*h^3 - 768*T0^8*Ud*a^3*d^4 + 768*T0^6*a^2*d^4*h^2 + 768*T0^4*Ud^2*a^2*d^4 + 256*T0^12*a^4*d^4 - 256*Ud^3*a*d^4 + 27*d^4*h^4 - 18*d^2*h^2 - 8*d*h - 1, d)), y)
RootOf(X31^4*a - 4*T0*X31^3*a + 6*T0^2*X31^2*a - 4*T0^3*X31*a - X31*h + Ud, X31)

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