8y''+10y'+y=0
Assuming "y" is a variable | Use as instead

Input

8 y''(x) + 10 y'(x) + y(x) = 0

ODE names

Autonomous equation

8 y''(x) = -y(x) - 10 y'(x)
Autonomous equation »

Sturm-Liouville equation

d/(dx) (e^((5 x)/4) y'(x)) + 1/8 e^((5 x)/4) y(x) = 0
Sturm‐Liouville equation »

ODE classification

second-order linear ordinary differential equation

Alternate form

y''(x) = -(5 y'(x))/4 - y(x)/8

Differential equation solution

y(x) = c_1 e^(-1/8 (5 + sqrt(17)) x) + c_2 e^(1/8 (sqrt(17) - 5) x)

Plots of sample individual solutions

| | | | y(0) = 1 y'(0) = 0 | | | | y(0) = 0 y'(0) = 1

Sample solution family

(sampling y(0) and y'(0))

Possible Lagrangian

ℒ(y', y, x) = 1/2 (e^((5 x)/4) (y')^2 - 1/8 e^((5 x)/4) y^2)
POWERED BY THE WOLFRAM LANGUAGE