解题
积分(反导数)计算器导数计算器代数计算器矩阵计算器更多的...
图表
线图指数图二次图正弦图更多的...
计算器
体质指数计算器复利计算器百分比计算器加速度计算器更多的...
几何
勾股定理计算器圆形面积计算器等腰三角形计算器三角形计算器更多的...
AI Chat
工具
笔记簿小组主题工作表练习验证
zs
English
Español
Português
Français
Deutsch
Italiano
Русский
中文(简体)
한국어
日本語
Tiếng Việt
עברית
العربية
受欢迎的 微积分 >

(e^y+1)^2e^{-y}dx+(e^x+1)^3dy=0

  • 初等代数
  • 代数
  • 微积分入门
  • 微积分
  • 函数
  • 线性代数
  • 三角
  • 统计
  • 化学

解答

(ey+1)2e−ydx+(ex+1)3dy=0

解答

y=ln(2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32xex2​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ln(ex+1)ex2​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32c1​ex2​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ex2​+2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−34xex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−34ln(ex+1)ex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−34c1​ex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ln(ex+1)​+2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32x​+2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−31​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32c1​​)
求解步骤
(ey+1)2e−ydx+(ex+1)3dy=0
求解可分离方程:y=ln(2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32xex2​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ln(ex+1)ex2​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32c1​ex2​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ex2​+2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−34xex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−34ln(ex+1)ex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−34c1​ex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ln(ex+1)​+2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32x​+2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−31​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32c1​​)
y=ln(2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32xex2​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ln(ex+1)ex2​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32c1​ex2​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ex2​+2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−34xex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−34ln(ex+1)ex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−34c1​ex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ex​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32ln(ex+1)​+2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32x​+2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−31​−2c1​+2ln(1+ex)+2ln(1+ex)ex2+2c1​ex2+4ln(1+ex)ex+4c1​ex−2x−2xex2−2ex−4xex−32c1​​)

作图

Sorry, your browser does not support this application
查看交互式图形

流行的例子

integral of 4e^x+12x^3+4x∫4ex+12x3+4xdxtangent f(x)=2sin(x),\at x= pi/4tangentf(x)=2sin(x),atx=4π​斜率 (5.2)(-9.6)slope(5.2)(−9.6)derivative e^{x^2-x}derivativeex2−x斜率 y=3+4x^2-2x^3x=aslopey=3+4x2−2x3x=a
学习工具人工智能数学求解器AI Chat工作表练习主题计算器作图计算器几何计算器验证解决方案
应用Symbolab 应用程序 (Android)作图计算器 (Android)练习 (Android)Symbolab 应用程序 (iOS)作图计算器 (iOS)练习 (iOS)Chrome 扩展程序
公司关于 Symbolab日志帮助
合法的隐私权Service TermsCookie 政策Cookie 设置请勿出售或分享我的个人信息版权、社区准则、DSA 和其他法律资源Learneo 法律中心
社交媒体
Symbolab, a Learneo, Inc. business
© Learneo, Inc. 2024