[已解决] 关联函数求导原函数

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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)

最佳答案


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
  1. clear; clc; close all;
  2. syms x f( x ) g( x )
  3. f = diff( g( x ), x );
  4. Eq = g * f == x * exp( x ) / ( 2 * ( 1 + x )^2 );
  5. G = dsolve( Eq )
  6. 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))

回复此楼

2 条回复


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
  1. clear; clc; close all;
  2. syms x f( x ) g( x )
  3. f = diff( g( x ), x );
  4. Eq = g * f == x * exp( x ) / ( 2 * ( 1 + x )^2 );
  5. G = dsolve( Eq )
  6. 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))

回复此楼

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