We have the following differential equation uu''=1+(u')^2 i found that the general

jazzcutie0h 2021-11-19 Answered
We have the following differential equation
=1+(u)2
i found that the general solution of this equation is
u=dcosh((xbd)
where b and d are constats
Please how we found this general solution?
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Expert Answer

Alicia Washington
Answered 2021-11-20 Author has 23 answers
You can separate that equation as
2uu1+u2=2uu
where both sides are complete differentials which integrate to
ln(1+u2)=ln(u2)+c1+u2=Cu2
Can you continue?
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Ourst1977
Answered 2021-11-21 Author has 21 answers
=1+(u)2
Substitute p=u
udpdx=1+p2
udpdududx=1+p2
udpdup=1+p2
Now it's separable
pdp1+p2=duu
It should be easy to integrate now..
Edit
p2+1=Ku2duKu21=±x+K2
arcosh(Ku}{K}=x+K2
Taking cosh on both side
Ku=cosh(K(x+K2))
u=1Kcosh(Kx+K2)
Which is close to your formula
u=dcosh(xbd)d=1K and bd=K2
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