Math Assignment | Importance of Pendulum in Science

Running head: MATH ASSIGNMENT 1
Math Assignment
Name
Institution

MATH ASSIGNMENT 2
Math Assignment
The equation is a first order differential equation (separable ODE) of the form
N ( y ) dy=M (x)dx
To solve it, we let y be an independent variable and divide it by dx to get:
1+2 xy d
dx ( y ) + y d
dx ( y )=e− y2
Writing it in the form N ( y ) dy=M (x)dx
N ( y )= y
−e− y2
+1 and M ( x ) = −1
2 x+ 1
y
−e− y2
+1
d
dx ( y )= −1
2 x +1
If N ( y ) dy=M ( x)dx then it means that ∫ N ( y ) dy=∫ M ( x )dx
∫ y
−e− y2
+1 dy =∫ −1
2 x +1 dx
Integrating ∫ −1
2 x+1 dx let 2 x+1=u then ∫ −1
2 x+1 dx=∫−2 udu=−ln ( 2 x+1 )
2 +C1
Integrating ∫ y
−e− y2
+1 dy, let y2=u
So that ∫ y
−e− y2
+1 dy =1
2 ∫ 1
−e−u +1 du
Let −u=v