Final answer:
To find the general solution of the given higher-order differential equation, d²y + 40 + 25y = 0, rewrite the equation as a characteristic equation and solve the quadratic equation to find the roots. Use the roots to determine the general solution of the differential equation.
Step-by-step explanation:
To find the general solution of the given higher-order differential equation, d²y + 40 + 25y = 0, we first rewrite the equation as a characteristic equation:
r² + 40r + 25 = 0.
We can solve this quadratic equation to find the roots (values of r). Once we have the roots, we can use them to determine the general solution of the differential equation.
For example, if the roots are r1 and r2, the general solution would be y = c1*e^(r1*x) + c2*e^(r2*x), where c1 and c2 are constants.