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# [已解决] 关联函数求导原函数

Travel_yer 发表于 2020-11-26 22:42:36
 MATLAB新人 想用MATLAB解答数学题 设X≥0时，g(x)＞，g(x)'=f(x),f(x)*g(x) = (x*exp(x))/(2*(x + 1)^2) syms x syms x f(x) syms x g(x) g(x)==diff(f(x),x) f(x)=(x)*exp(x)/2/(1+(x))^2/g(x)

TouAkira 发表于 2020-11-27 03:43:03
 本帖最后由 TouAkira 于 2020-11-26 15:49 编辑 直接 clear; clc; close all; syms x f( x ) g( x ) f = diff( g( x ), x ); Eq = g * f == x * exp( x ) / ( 2 * ( 1 + x )^2 ); G = dsolve( Eq ) F = diff( G, x )复制代码 G =   (2*C1 + exp(x) + 2*C1*x)^(1/2)/(x + 1)^(1/2) -(2*C1 + exp(x) + 2*C1*x)^(1/2)/(x + 1)^(1/2) F = (2*C1 + exp(x))/(2*(x + 1)^(1/2)*(2*C1 + exp(x) + 2*C1*x)^(1/2)) - (2*C1 + exp(x) + 2*C1*x)^(1/2)/(2*(x + 1)^(3/2)) (2*C1 + exp(x) + 2*C1*x)^(1/2)/(2*(x + 1)^(3/2)) - (2*C1 + exp(x))/(2*(x + 1)^(1/2)*(2*C1 + exp(x) + 2*C1*x)^(1/2))

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TouAkira 发表于 2020-11-27 03:43:03
 本帖最后由 TouAkira 于 2020-11-26 15:49 编辑 直接 clear; clc; close all; syms x f( x ) g( x ) f = diff( g( x ), x ); Eq = g * f == x * exp( x ) / ( 2 * ( 1 + x )^2 ); G = dsolve( Eq ) F = diff( G, x )复制代码 G =   (2*C1 + exp(x) + 2*C1*x)^(1/2)/(x + 1)^(1/2) -(2*C1 + exp(x) + 2*C1*x)^(1/2)/(x + 1)^(1/2) F = (2*C1 + exp(x))/(2*(x + 1)^(1/2)*(2*C1 + exp(x) + 2*C1*x)^(1/2)) - (2*C1 + exp(x) + 2*C1*x)^(1/2)/(2*(x + 1)^(3/2)) (2*C1 + exp(x) + 2*C1*x)^(1/2)/(2*(x + 1)^(3/2)) - (2*C1 + exp(x))/(2*(x + 1)^(1/2)*(2*C1 + exp(x) + 2*C1*x)^(1/2))

Travel_yer 发表于 2020-11-27 15:23:48
 感谢帮助
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