Answer:
The solution to the differential equation
y' = 1 + y²
is
y = tan x
Step-by-step explanation:
Given the differential equation
This can be written as
dy/dx = 1 + y²
Separate the variables
dy/(1 + y²) = dx
Integrate both sides
tan^(-1)y = x + c
y = tan(x+c)
Using the initial condition
y(0) = 0
0 = tan(0 + c)
tan c = 0
c = tan^(-1) 0 = 0
53
-30x+147= -171-24x
+24x +24x
-6x+147= -171
-147 -147
-6x= -318
x=53
Hope this helps!