Differential Equations

F(s) = L{(1)} (s)

• 1/s

• n!/s⁽ⁿ⁺¹⁾

• 1/(s-a)

• n!/(s-a)⁽ⁿ⁺¹⁾

• s/(s²+b²)

F(s) = L{(tⁿ)} (s)

• 1/s

• n!/s⁽ⁿ⁺¹⁾

• 1/(s-a)

• n!/(s-a)⁽ⁿ⁺¹⁾

• s/(s²+b²)

F(s) = L{(e^at)} (s)

• 1/s

• n!/s⁽ⁿ⁺¹⁾

• 1/(s-a)

• n!/(s-a)⁽ⁿ⁺¹⁾

• s/(s²+b²)

F(s) = L{(tⁿe^at)} (s)

• 1/s

• n!/s⁽ⁿ⁺¹⁾

• 1/(s-a)

• n!/(s-a)⁽ⁿ⁺¹⁾

• s/(s²+b²)

F(s) = L{(cos(bt))} (s)

• 1/s

• n!/s⁽ⁿ⁺¹⁾

• 1/(s-a)

• n!/(s-a)⁽ⁿ⁺¹⁾

• s/(s²+b²)

F(s) = L{(sin(bt))} (s)

• 1/s

• b/(s-a)² + b²

• (s-a)/(s-a)²+b²

• b/(s² + b²)

• s/(s²+b²)

F(s) = L{(e^atsin(bt))} (s)

• 1/s

• b/(s-a)² + b²

• (s-a)/(s-a)²+b²

• b/(s² + b²)

• s/(s²+b²)

F(s) = L{(e^atcos(bt))} (s)

• 1/s

• b/(s-a)² + b²

• (s-a)/((s-a)²+b²)

• b/(s² + b²)

• s/(s²+b²)

Linearity Formula

Input derivative principles