- #1
Dusty912
- 149
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Homework Statement
Question: Solve this differential equation
dy/dt=1+y2 and y(π/4)=-1
Homework Equations
The Attempt at a Solution
dy/dt=1+y2 and y(π/4)=-1
dy/dt=1+y2
dy=(1+y2)dt
dy/(1+y2)=dt
∫dy(1+y2)=∫dt
tan-1(y)=t+c
y(t)=tan(t)+c
y(π/4)=tan(π/4)+c
-1=1+c
-2=c
answer: y(t)=tan(t)-2