Exercise: Separate the variables and solve. 1. x(2y-3)dx+(x²+1)dy=0 ans: (x²+1)(2y-3)=Fc

Q: 2. Use separation of variables to solve the following equations: (a) (y² + 1)dy + (e² + x)dx = 0.

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Q: Solve the Cauchy euler equation d³y x3 dx3 3x2 d?y dx2 2 + 6x -6y = 3 + Inx³ dy dx

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Q: Specify if it is exact or non-exact. Find the general solution. (y^2-2xy+6y) dx - (x^2 -2xy +2) dy…

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Q: Solve the IVP (2xy?+4)=2(3-x²y)- y(-1)%3D8 the constant Cis dx

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Q: (x +2y-4) dx + (ax-4y ) ay Solve by Coerlaents linear in two variable

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Q: Consider the equation, test whether it is exact and solve the IVP.        x(x-y)dy = y(y-3x)dx…

A: solGivenx(x-y)dy=y(y-3x)dx

Q: d?y Example: Solve the D.E. + 2 dx2 dy + 2y = 0 dx

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Q: dy = -8xy² dx 3. Solve + 4x(4x+1) y-(8.x² +4x² -1) by knowing u =x is a solution.

A: Given: dydx=-8xy2+4x4x+1y-8x3+4x2-1

Q: 3. Obtain the general solution 3 3 y.(x .y + 2-x – y) dx+ 3 - 2).dy = 0 x (xy |

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Q: Solve the order linear equation, dy dy 1 +-y=x, y(1) =5 dx x + p(x)y=r(x) dx x 14 + Solution: y= 3…

A: The initial condition in an initial value problem is used to determine the integration constant that…

Q: solve the DE b

A: The DE is (x-y+2)dx-dy=0or, (x-y+2)dx=dyor,dydx=x-y+2

Q: noose a non-exact equation and solve. (xy - 2y?)dx - (x2 - 3xy)dy=D0 1. 2)

A: Q(1)  We have to solve given non exact differential equation:

Q: Consider the equation, test whether it is exact and solve the IVP.        x(x-y)dy = y(y-3x)dx…

A: Solution:  Step I:    xx-y dy =yy-3xdx     y-1=1 Now,    xx-y dy=yy-3x  dx    dydx=yy-3xxx-y  Let…

Q: Check whether the given first order linear diff equation is homogenous or exact or separable or none…

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Q: A. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS d³x 3. dt3 d?x -2 dx - 35 = 0 dt 4. (D³ – 4D² + 4D)y…

A: To find the solution of homogenous linear equation with constant coefficient we assume the trial…

Q: Quiz Solve a Bernoulli's equation. dx 2X dy vg (x

A: The detailed solution is as follows below:

Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: How To Solve It? Which Method? dy/dx-dx/dy= x/y- y/x

A: ∫(1/y) dy  =log y +c ∫ (1/x)dx = log x +c  ∫  ydy  =(y2)/2   +c  ∫ xdx   = (x2)/2   +c log(a)+log (b…

Q: dy 4у dx х (у-3)

A: Given query is to find the soly of the differential equation.

Q: Test For Exactness, if Exact, solve. 1. (3x2y+2e2y+3)dx + (x3+4xe2y-sech2y+2lny-y)dy=0

A: The equation is exact as My=Nx, and the solution follows as:

Q: 2. Obtain the general solution using Bernoulli's equation. Simplify your final answer. + x dx - –…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the equation: (x-2y) dx + 2(y-x) dy = 0 Answers should be within these givens. x2 – xy + 4y2…

A: Let's find.

Q: Find the solution. d3x d?x dx – 2–=0 dt + dt3 di2 -21 ® y = c,+c,e'+c,e- -31 D y = c,++ce+c,e-2

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Q: Solve the Euler equation d²y dy 3x? dx -5у%3D0 +x dx given that y(1) =1 and y'(1) = 2.

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Q: Exercise: Find the general solution of (x² – xy + y²)dx – xydy = 0

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Q: Using Variable Separable, solve x² (y + 1) dx + y² ( x − 1) dy = 0

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Q: Using Homogeneous Equations, find the general solution of the equation below. dy dx x-y y

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Q: Solve the equation dy + 4xy dx = 2x dx Answer should be within the givens: ye2x^2 = ½ e2x^2 + C…

A: We have to find the general solution of the differential equation dy + 4xy dx = 2x dx.

Q: Solve the equation 3x(xy – 2)dx + (x³ + 2y)dy = 0 ƏM = 3x2 ду Ne 3x2 Sol/ əx f(x, y) = (3x²y – 6x)dx…

A: From the given differential equation: 3xxy-2dx+x3+2ydy=0 As we know that the differential equation…

Q: 2. Obtain the particular solution when x = 1 and y = 1 y(? - y? + 1) dx – x(x² - y? - 1) dy = xlx? -…

A: Here is the solution of the given differential equation.

Q: The solution of D.E " -y = 5(t – 1) ,y(0) = 0,y'(0) = 0

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Q: What is the general solution of ху(ху5 - 1) dx + х?(1+ ху)dy3D0 ? A 2x3y5-3x² = cy? B 2x°y3 - 3x2 =…

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Q: (4x® y-18x² + y)dx+(x* + 3y +x)dy= 0

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Q: Exercise 5 Using the method of variation of parameters, the particular solution , for y"+3 + 2y = "…

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Q: #3 Test the exactness and solve the equation. (2xy 3x²)dx + (x² + y)dy = 0

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Q: Solve the exact equation + 2x )dx + + 2y )dy 0. The solutions are of the form F(x, y) c, where %3D…

A: Given;

Q: Solve 5 2 E #(0) = – 2, y(0) = = 10 | Ly' - 29 - x(t) = %3D y(t) =

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Q: (c) Test for exactness and solve the IVP, critically outline the particular solution (x + 5e*y)dx =…

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Q: What is the general solution of e3x dx? J (1 – 2e3= )2

A: Use substitution t=1-2e^(3x)

Q: (x+2y-1)dx+(5-2x-y)dy=0; y(0)=0, implicit solution  Also: a) Value of y if x=2

A: By arranging the question and then taking boldfaced ratio we'll get the answer. Here,I am providing…

Q: 2. Solve (y 2)dx (x- y 1)dy 0 using the method for linear coefficients in two linear variables. %3D…

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Q: dy 2хy dx y2 + y?e6). +2x2e

A: We have to Verify if homogenous equation then solve for general solution​As per given question

Q: 3-x If j- dx = x(x – 1)(x +2) +. x+2 When A, B, and C are solved, what is the value of their sum or…

A: Given ∫3−xxx−1x+2dx=∫Ax+Bx−1+Cx+2dx.....1 We have to find the value of A+B+C. Take partial fraction…

Q: Solve the diffrential equation.(pls step bu step and clearly) (d/dx+2x)(dy/dx+2xy)=2e^(-x^2)

A: We have given differential equation is…

Q: (Think homogeneous) Solve explicitly (y² - xy) dx + x²2dy = 0

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Q: (2xy - x + 2y - 1) dx + (8x² y² -2x + 4xy2 - x) dy = 0

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Q: (15pts) Identify (write down) the type of DE, and find the general solution. (y- 3x)dy = (x +3y)dx…

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Q: PART - B IA. Solve (4xy + 3y? - x)dx + x(x +2y)dy = 0 with y(2)=2. IB. Solve (x²D2 + xD - 1)y =ri

A: Since, you have posted multiple questions. As per guidelines we will solve only first question. If…

Q: (2xy - x + 2y - 1) dx + (4x²y² - x² + 4xy² - x) dy = 0

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