Find Differential Equation by eliminating arbitrary constant from y=x+c1e^x+c2e^-x?
- az_lenderLv 72 months ago
dy/dx = 1 + c1*e^x - c2*e^(-x);
d2y/dx2 = c1*e^x + c2*e^(-x) = y - x.
The differential equation y" = y-x
has y = x + c1*e^x + c2*e^(-x) as a solution.
The only thing wrong with Katherine Malakowski's answer is her error in typing the first derivative (there should be a 1 in it).
- VamanLv 72 months ago
take the first derivative.
dy/dx= c1 e^x-c2 e^x. Take the second derivative.
d^2y/dx^2= c1 e^x + c2 e^-x. Eliminate using the first equation.
d^2y/dx^2=y-x. You can write it as y'' -y=-x. This is the differential equation.
- Anonymous2 months ago