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In Problems 11–16, determine whether the differential equation can be written in the separation of variables form
11.
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- One of the below is a condition of a linear differential equation. A. dependent variable and its derivative are of degree greater than one B. Term coefficients should be dependent on the unknown variable C. coefficients of a term does not depend upon dependent variable D. all derivative process should be in terms of the constant variablearrow_forwardIn Problems 1–18 solve each differential equation by variation of parameters.y''+3y'+2y=sin(e^x)arrow_forwardNumber 22 onlyarrow_forward
- State the order of the given ordinary differential equation. (1 - x)y" – 9xy' + 5y = cos x Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. dy + a,(x)y = g(x) (6) + a + · . . + a, (X) dx" - 1 dx O linear nonlineararrow_forwardState the order of the given ordinary differential equation. (1-x)y" - 3xy' + 6y = cos x Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1.1 (x) any + an +...+ dxn ly -1(x) an dx-1 + a₁(x) dx + + a(x) = g(x) (6) dx O linear O nonlinear harrow_forwardwhich is the solution of the differential equationarrow_forward
- 2. Find the differential equation of all straight lines at 2- unit distance from the origin.arrow_forward23. By suitably renaming the constants and dependent variables in the equations and T'=k(T-Tm) G' = -XG+r discussed in Section 1.2 in connection with Newton's law of cooling and absorption of glucose in the body, we can write both as y' = -ay+b, (A) (B) (C) where a is a positive constant and b is an arbitrary constant. Thus, (A) is of the form (C) with y = T, a = k, and b = kT, and (B) is of the form (C) with y = G, a = λ, and b = r. We'll encounter equations of the form (C) in many other applications in Chapter 2. Choose a positive a and an arbitrary b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0≤t≤T, c≤y≤d} of the ty-plane. Vary T, c, and d until you discover a common property of all the solutions of (C). Repeat this experiment with various choices of a and b until you can state this property precisely in terms of a and b.arrow_forward4. dr 0, x(0) = 1, x'(0) ; (0) - 3, x(0) = -1arrow_forward
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