1. Identify each of the following equations as linear or nonlinear and also determine their order...
Match the third order linear equations with their fundamental solution sets. 1. y????y???y?+y=0 2. y????5y??+6y?=0 3. y???+3y??+3y?+y=0 4. ty????y??=0 5. y???+y?=0 6.y????2y??+y??2y=0 A. 1, cos(t), sin(t) B. e?t, te?t, t2e?t C. 1, e3t, e2t D. e2t, cos(t), sin(t) E. et, tet, e?t F. 1, t, t3
1. For each of the following differential equations, state their order and if they are linear or nonlinear: (a) y" + sin(t)y = cos(t) (b) cos(t) + sin(y)t =y"
Determine the order of the given differential equations; also state whether the equation is linear or nonlinear. w (a). y = (sin t)y (b). (2 + y)y" – 4y = cos 3x.
1. (12 points) Classify the following equations as lincar or nonlinear, and state their order. Linear or nonlincar? Order Equation + tdk + t'y = cost they + t dope + t'y = cosy. dy 2y-2
(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...
1.7-1 For the systems described by the equations below, with the input f(t) and output v(t), determine which of the systems are linear and which are nonlinear. dy dt (a) + 2y(t)-f(t) (b) +3y() -se) (e) ( ) +2y(t)-f(t) (d) +92(t) = f(t) (c) 3y(t) + 2 = f(t) (f) + (sin t)y(t)-2 + 2/(t) dt dt (h) v(t)f(r)dr dt
(17 points) Match the third order linear equations with their fundamental solution sets. 1. y" + 3y" + 3y + y=0 2. Y" - 8y" + 15y = 0 3. y" - y" - y' + y = 0 4. ty" - y = 0 5. y" + y = 0 6. y" – 3y" + y - 3y = 0 est A. 1, e3t, B. e3t, cos(t), sin(t) c.1, t, 13 D. 1, cos(t), sin(t) E. e , te,...
(17 points) Match the third order linear equations with their fundamental solution sets. 1. y" - Y" - ' +y=0 2. y'" - 5y" + 6y' = 0 3. ty" - y" = 0 4. Y" + y 0 5.Y" - 6y" + y - by = 0 6. Y" + 3y" + 3y + y=0 A. e , te, tet B. e, cos(t), sin(t) C. 1, cos(t), sin(t) D. 1, t, 13 E. et, tet, et F. 1, 2,...
1. Classify each ordinary differential equation as to order (1st, 2nd, etc) and type (linear/nonlinear). a) y' + 2y + 3y = 0 b) y" + 2yy + 3y = 0 c) y" + 2y' + 3xy - 4e" y sin 3
for differential equations 1. Identify each of the following differential equations as either Separable, Homogeneous, Linear Bernoulli, or Exact and solve the equation using the method of the type you have identified. Many can be classified in multiple ways, it is not necessary to list all possibilities. (3xy2 +2ycos x)+y'-y sin x-x =0 Туре: A. dx General Solution: B. (4xy+xy)2x+ xy2 dx Туре: General Solution: Туре: C. y'y'y+1 General Solution: (3x'y+e')-(2y-x-xe)dy Туре: D. dx General Solution: Туре: dy E. =y(xy-1)...