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Solutions to Simple Differential Equations, Summaries of Mathematics

Mathematics

The solutions to five simple differential equations. Each equation is given in the form of dy/dx = f(x,y), and the final answer is presented as dy/dx = mx/ny, where m and n are constants. These solutions can be useful for students and researchers in mathematics, physics, and engineering.

Typology: Summaries

2018/2019

Uploaded on 09/24/2022

dukenilo
dukenilo 🇵🇭

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bg1
1. x^2 + y^2 = 18
= 2x + 2y dy/dx = 18
-2x -2x
= 2y dy/dx = 16x
2y 2y
Final Answer= dy/dx = 8x/y
2. 2x + 7y = 9
= 2x + 7y dy/dx = 9
-2x -2x
= 7y dy/dx = 7x
7y 7y
Final Answer= dy/dx = x/y
3. x^2 + 4y = 16
= 2x + 4y dy/dx = 16
-2x -2x
=4y dy/dx = 14x
4y 4y
Final Answer = dy/dx = 7x/2y
4. 4x^2 + 9y^2 = 36
= 8x + 18y dy/dx = 36
-8x -8x
= 18y dy/dx = 28x
pf2

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  1. x^2 + y^2 = 18 = 2x + 2y dy/dx = 18 -2x -2x = 2y dy/dx = 16x 2y 2y Final Answer= dy/dx = 8x/y
  2. 2x + 7y = 9 = 2x + 7y dy/dx = 9 -2x -2x = 7y dy/dx = 7x 7y 7y Final Answer= dy/dx = x/y
  3. x^2 + 4y = 16 = 2x + 4y dy/dx = 16 -2x -2x =4y dy/dx = 14x 4y 4y Final Answer = dy/dx = 7x/2y
  4. 4x^2 + 9y^2 = 36 = 8x + 18y dy/dx = 36 -8x -8x = 18y dy/dx = 28x

18y 18y Final Answer = dy/dx = 14x/9y

  1. y - x^2 + 2x = 0 = y dy/dx – 2x + 2x = 0 2x 2x = y dy/dx +2x = 2x -2x -2x Final Answer = y dy/dx = x