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Popular >

(d^2-1)y=sech(x)

Solution

(d^{2} - 1) y = sech (x)

Solution

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x} sech ( x )}{2} d x + e^{- x} (- \frac{1}{2} e^{x} sech (x) + \frac{1}{2} sech (x) arcsech (sech (x)) + arcsin (\frac{2}{2} sech (x) + 1))

Solution steps

(d^{2} - 1) y = sech (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x} sech ( x )}{2} d x + e^{- x} (- \frac{1}{2} e^{x} sech (x) + \frac{1}{2} sech (x) arcsech (sech (x)) + arcsin (\frac{2}{2} sech (x) + 1))

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x} sech ( x )}{2} d x + e^{- x} (- \frac{1}{2} e^{x} sech (x) + \frac{1}{2} sech (x) arcsech (sech (x)) + arcsin (\frac{2}{2} sech (x) + 1))

Popular Examples

(d+2)*(d-1)^3*y=e^x

(d + 2) \cdot (d - 1)^{3} \cdot y = e^{x}

y^{'''}-2y^{''}+y^'=2-24e^x+40e^5x

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 2 - 24 e^{x} + 40 e^{5} x

(d^{2} + 9) y = 2 x^{2}

(d^5-d)*j=8sin(x)-2*x

(d^{5} - d) \cdot j = 8 sin (x) - 2 \cdot x

y^{'''}+2y^{''}=12x^5

y^{^{'''}} + 2 y^{^{''}} = 12 x^{5}

Frequently Asked Questions (FAQ)

What is the solution for (d^2-1)y=sech(x) ?
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