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1. Classify each ordinary differential equation as to order (1st, 2nd, etc) and type (linear/nonlinear). a)...
Find a first-order system of ordinary differential equations equivalent to the second-order nonlinear ordinary differential equation y ^-- = 3y 0 + (y 3 − y) (3 points) Find a first-order system of ordinary differential equations equivalent to the second-order nonlinear ordinary differential equation y" = 3y' +(y3 – y).
3.1. For each of the following ordinary differential equations, determine its order and whether or not it is linear: a. 3xy"-xy'+ 2y= sin x b. (2 - y(dyldx)- x(dyldx)+ y e c. y"+(cosx)y" 3y'- (cosx)y x d. y"-(y2y 0.
non-homo 2nd order linear equations 1. Find the general solution for each of the following differential equations (10 points each): (a) (b) (e) y" – 2y! - 3y = 3e2x y" — y' – 2y = -2.3 + 4.2? y" + y’ – 67 = 1234 + 12e-2x y" – 2y' – 3y = 3.ce-1 y" + 2y' + y = 2e- (Hint: you'll use Rule 7. at least once) (e 2. Find the solution to the following differential equation...
(1 point) It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved...
1. Identify each of the following equations as linear or nonlinear and also determine their order dy (a) y = t 3 3 (b) ( dy + (c) sin t (d) (1y) sin t ( cos2 t 1 y sin(t)= 0 (e) Int +3etdy dt (f) 2y'-y2 =e (g) y"(t2 1)y+cos(t (h) y"sin(ty)y(t21)y 0 = 0 1. Identify each of the following equations as linear or nonlinear and also determine their order dy (a) y = t 3 3 (b)...
Classify each equation as linear or nonlinear dy/dx = y^3 - 9 linear y" = 3y' - 6 nonlinear > 3y y' = 6-4 linear > 4x^2 y" - 3x y' + 4y = 2x - 4 linear
Question 2 (1 point) Saved Classify the differential equation by order and linearity. dy co3y sin (2t COS Nonlinear, second order differential equation Linear, first order differential equation Nonlinear, first order differential equation Linear, second order differential equation
II. Determine the general solution of the given 2nd order linear homogeneous equation. 1. y" - 2y' + 3y = 0 (ans. y = ci e' cos V2 x + C2 e* sin V2 x) 2. y" + y' - 2y = 0 (ans. y = C1 ex + C2 e -2x) 3. y" + 6y' + 9y = 0 (ans. y = C1 e 3x + c2x e-3x) 4. Y" + 4y = 0, y(t) = 0, y'(T) =...
dy 4. (a) Classify the following differential equation: +yrsin(a) i. ORDER ii. LINEAR/NONLINEAR: iii. SEPARABLE/NOT SEPARABLE: (b) Use your classification from (a) to use an appropriate method in the following problem. Be sure to clearly label steps to maximize your score Find an explicit solution of +y=sin(x). Explicit Solution: (c) Give the largest interval over which the general solution is defined. (d) Are there any transient terms in the general solution? If yes, what are they?
State the order of the following ordinary differential equations and classify them as linear or non-linear. (2t-e2t) day +64 dy dt4 dt = - ye-66 + 2sin(5t) The order of the differential equation is and it is ---Select--- d²f dp2 = pln(-6p) + 2e5p The order of the differential equation is and it is ---Select--- day sinh( ) – In(6) dy dx = 2cos(5y) – y dx2 The order of the differential equation is and it is ---Select---