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6.5. Equations With Hyperbolic Nonlinearity
6.5-1. Integrands With Nonlinearity of the Form cosh[βy(t)]
b
1. y(x)+ A cosh[βy(t)] dt = g(x).
a
This is a special case of equation 6.8.27 with f(t, y)= A cosh(βy).
b
µ
k
2. y(x)+ A t cosh [βy(t)] dt = g(x).
a
k
µ
This is a special case of equation 6.8.27 with f(t, y)= At cosh (βy).
b
3. y(x)+ A cosh(µt) cosh[βy(t)] dt = g(x).
a
This is a special case of equation 6.8.27 with f(t, y)= A cosh(µt) cosh(βy).
b
4. y(x)+ A e λ(x–t) cosh[βy(t)] dt = g(x).
a
This is a special case of equation 6.8.28 with f(t, y)= A cosh(βy).
b
5. y(x)+ g(x) cosh[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.29 with f(t, y) = cosh(βy).
b
6. y(x)+ A cosh(λx + µt) cosh[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.31 with f(t, y)= A cosh(βy).
b
7. y(x)+ A sinh(λx + µt) cosh[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.32 with f(t, y)= A cosh(βy).
b
8. y(x)+ A cos(λx + µt) cosh[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.33 with f(t, y)= A cosh(βy).
b
9. y(x)+ A sin(λx + µt) cosh[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.34 with f(t, y)= A cosh(βy).
6.5-2. Integrands With Nonlinearity of the Form sinh[βy(t)]
b
10. y(x)+ A sinh[βy(t)] dt = g(x).
a
This is a special case of equation 6.8.27 with f(t, y)= A sinh(βy).
© 1998 by CRC Press LLC
© 1998 by CRC Press LLC
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