What is a solution to the differential equation \frac{dy}{dx}=y^{2}+1 with

runddansm88e

runddansm88e

Answered question

2022-04-17

What is a solution to the differential equation dydx=y2+1 with y(1)=0?

Answer & Explanation

Emelia Leon

Emelia Leon

Beginner2022-04-18Added 18 answers

dydx=y2+1
grouping variables
dyy2+1=dx
Integrating both sides
arctan(y)=x+C
then
y=tan(x+C)
Now, observing the initial condition
y(1)=tan(1+C)=0 so
1+C=0+kπ,k=±1,±2,
and concluding
y=tan(x1)

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