How to eliminate arbitrary constants

y=C1e^x+C2e^2x+C3e^3x

thank you :)

September 3, 2017 - 5:02pm

#1
EngineerInTheMaking

Differential Equation: Eliminate C1, C2, and C3 from y=C1e^x+C2e^2x+C3e^3x

How to eliminate arbitrary constants

y=C1e^x+C2e^2x+C3e^3x

thank you :)

Subscribe to MATHalino.com on

We're now on YouTube! Please subscribe.

- Family of Plane Curves
- Decimal Fractional Parts of Dim's on Hypotenuses of Dissimilar Right Triangles
- Acceleration of Riged body (flyweight) with forces
- Cables and Arches
- Trigo sin cos tan sec csc cot
- Arithmetic sequence
- Round off 314.587321 into four significant figures
- algebra 1
- Concavity calculus
- Problem 126 explanation please

- Family of Plane Curves
- Acceleration of Riged body (flyweight) with forces
- Trigo sin cos tan sec csc cot
- Concavity calculus
- Problem 126 explanation please
- Finding the sum of sequence
- Decimal Fractional Parts of Dim's on Hypotenuses of Dissimilar Right Triangles
- Product of Areas of Three Dissimilar Right Triangles
- Area of Right Triangle Using Radius of Incircle
- The Formula for the Curve of a Trumpet Bell

$y = C_1 e^x + C_2 e^{2x} + C_3 e^{3x}$ ← Equation (1)

$y' = C_1 e^x + 2C_2 e^{2x} + 3C_3 e^{3x}$ ← Equation (2)

$y'' = C_1 e^x + 4C_2 e^{2x} + 9C_3 e^{3x}$ ← Equation (3)

$y''' = C_1 e^x + 8C_2 e^{2x} + 27C_3 e^{3x}$ ← Equation (4)

Equation (2) - 3 × Equation (1)

$y' - 3y = -2C_1 e^x - C_2 e^{2x}$ ← Equation (5)

Equation (3) - 3 × Equation (2)

$y'' - 3y' = -2C_1 e^x - 2C_2 e^{2x}$ ← Equation (6)

Equation (4) - 3 × Equation (3)

$y''' - 3y'' = -2C_1 e^x - 4C_2 e^{2x}$ ← Equation (7)

Equation (6) - 2 × Equation (5)

$(y'' - 3y') - 2(y' - 3y) = 2C_1 e^x$ ← Equation (8)

Equation (7) - 2 × Equation (6)

$(y''' - 3y'') - 2(y'' - 3y') = 2C_1 e^x$ ← Equation (9)

Equation (9) - Equation (8)

$[ \, (y''' - 3y'') - 2(y'' - 3y') \, ] - [ \, (y'' - 3y') - 2(y' - 3y) \, ] = 0$

$(y''' - 5y'' + 3y') - (y'' - 5y' + 3y) = 0$

$y''' - 6y'' + 8y' - 3y = 0$