Yc1e3xc2e4xSolutionI believe this is the solution of a diffe

Y=c₁e^3x+c₂e^-4x

I believe this is the solution of a differential equation and you are supposed to find the corresponding differential equation.

Given solution:

Y=c₁e^3x+c₂e^-4x

Therefore, roots of characteristic equation are -4 and 3. Therefore, characteristic equation is:

(m+4)(m-3)=0

m²+4m-3m-12=0

m²+m-12=0

Therefore, the required differential equation is:

y\'\'+y\'-12y=0