16. Identify the type of ODE below (ex. Separable, Linear, Exact, etc...) and then solve the...
17. Identify the type of ODE below (ex. Separable, Linear, Exact, etc...) and then solve the equation using the appropriate technique (give an explicit final answer in the form “y = ..."). You may assume x > 0. dy = x3 72 dx = xy - y2
Identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y alone (3x+3x - 3y)dx + (xy? - x-2)dy = 0 Select all that apply. A. has an integrating factor p(x) or p(y) not equal to a constant OB. linear OC. separable D. exact E. none of the above
Identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y alone. (4x+3x - 3y)dx + (xy3 – x-2)dy = 0 Select all that apply. A. exact B. has an integrating factor u(x) or (y) not equal to a constant C. linear D. separable E. none of the above
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)...
1. a) Solve the following linear ODE. dy * dx + 2y = 4x2, x > 0 b) Solve the following ODE using the substitution, u = dy (x - y) dx = y c) Solve the Bernoulli's ODE dy 1 + -y = dx = xy2 ; x > 0
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?
2. Find the general solution to the first-order linear differential equation dy ex x + 2y = dx by finding an appropriate integrating factor. (No credit for any other method). Give an explicit solution. =- X
Need help with all of it Problem 2: Consider the 1st order ODE ry + (2.+ 3y2 – 20y = 0. (2) As we discussed in class, this ODE isn't linear, exact, or separable. We will now develop a method to solve an ODE like this. Consider the more general case given by the ODE M(2,4) + N(2,4)} = 0 as in our situation, assume this ODE isn't linear, separable, or exact. Our goal will be to find a function...
Identify the type of the following differential equation. Note: y is the dependant variable in the equation. dy dx -2y 2 (4+lny-lnx) Select all that apply. Seperable Linear Exact Homogeneous Bernoulli Linear Substituion Identify the type of the following differential equation. Note: y is the dependant variable in the equation. 31/2 dy - 4 = y3/2 dx Select all that apply Seperable Linear Exact Homogeneous Bernoulli Linear Substituion dy The differential equation 6 - dx 949,6 – 24 can be...
In the previous lecture this method was explained. Recall that an ODE of the type dy/dr+py be rewritten as may 讐-劘塭 dr with ydl/dx- Ipy from where /(x) can be derived The complete solution of this ODE then is a sum of two terms: a term y. which is a solution of the ODE rewritten as d(ly)/dx- lq and a term y2, which follows from solving the homogeneous equation (the ODE with q-0 Task Solve two differential equations and determine...