If y_1, y_2, ..., y_n are linearly independent solutions to an nth- order homoge

Question

If y_1, y_2, ..., y_n are linearly independent solutions to an nth- order homogeneous linear differential equation with constant coefficients, then the general solution is given by y = c_1y_1 + c_2y_2 + ... + c_ny_n If y_1, y_2, ..., y_n are solutions to an nth-order homogeneous linear differential equation with constant coefficients, then so is y = c_1y_1 + c_2y_2 +... + c_ny_n Reduction of order is a technique for finding an additional solution to a homogeneous linear differential equation. If y_1, y_2, ..., y_n are linearly dependent, then it's possible to express one of the y_i's as a linear combination of the others. If Q is a function of t and the rate of change of Q is proportional to Q, then dQ/dt = kQ for some constant k. The ODE dy/dx = y^2 + 4 has two equilibrium points. A differential equation for which the unknown function involves two or more independent variables is called an ordinary differential equation. The integrating factor for the linear equation a(x)dy/dx + b (x) y = c(x) is mu(x) =_e integral b(x) dx. Some non-homogeneous first-order linear differential equations are separable. Euler's method is an example of a technique for approximating solutions to differential equations. Variation of parameters can be used to find the particular solution to a linear differential equation with constant coefficients and Cauchy-Euler equations. L^-1 {F(s) + G(s)} = f(t) + g(t)

Explanation / Answer

(a) True

(b) False

(c) True

(d) True

(e) True

(f) True

(g) False

(h) False

(i) False

(j) True

(k)

(l) True

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.