Check for exactness and obtain the general solution. 1. -x(4y3 – 3xy – 6)dx – (6x²y² + 1- x³)dy = 0

Q: 22) Solve the 2nd order differntial equation d2y 2y ax? dx² `dx' n terms of the integration…

A: Given equation is, Take, Then the equation becomes,

Q: k is the (6xy3 + cos y)dx+(3kx²y² – xsin y)dy = 0 exact? For what value of differential equation A 3…

A: To find out the value of k for which the differnet equation is exact.

Q: Solve the given initial-value problem. dy (x + 3) + y = In(x), y(1) = 25 dx х In(x) —х+ 51 y(x) =…

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Q: 15x²x343x - 19 The integral (x + 1)²(x² - 6x +13) can be rewritten as Slax [ax² + bx² + c + (mx +…

A: The objective is to determine ∫C(mx+n)t

Q: 2) Find the particular solution for the systen and intital values given below -35 x; X1(0) = 0,…

A: See the detailed solution below.

Q: 1. Find the order (write in number) for * y² d²y dx2 d5y 3x + 4x = 0. dx5 Your answer 2. + 4x = 0 is…

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Q: Which of the following differential equations can be solveusing determination ofintegrating factor?…

A: This is a differential equation question

Q: 5. Find the general solution of (6x² – 7y²) dx – 14xy dy = 0

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Q: Q1) Evaluate the value of the integral , e-5x In x² dx by using the Simpson's method, with n=6? اضف…

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

Q: Which differential equation follows the form A (x) dx +B(y) dy=0? ysinxdx-2xcosydy=0 B There is no…

A: Check for all the options.

Q: Solve the initial value problem = x', y (0) = 3. dy %3D dx (Use symbolic notation and fractions…

A: The given initial value problem,   dydx=x5 ;  y(0)=3

Q: Find all values of k for which the function y = sin(kt) satisfies the differential equation y' + 17y…

A: We find y" using the chain rule

Q: (a) For what values of k does the function y = cos(kt) satisfy the differential equation 100y 49y?…

A: Given y=cos(kt) satisfy the differential equation 100y"=-49y

Q: The following Differential Equation is exact. Use the fact that M(x,y)=F(x,y) and N(x,y)=F(x,y) in…

A: The following Differential Equation is exact.  Use the fact that M(x,y)=F(x,y) and N(x,y)=F(x,y) in…

Q: II. Determine the ORDER and the DEGREE of the following differential equations. d?y 4. x + y + 4y? =…

A: 4) For the given differential equation

Q: Which of the following should the function k(x) be in order for the solution of differential k(x)…

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Q: Which of the following is the general solution to the differential equa · (x – /x² + y² )dy = 0 ? dx…

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Q: Answer: -x sin(x²) # COS X Find the particular solution, y = f(x), dy to the differential equation…

A:

Q: (ii) Write a trial solution for the method of undetermined coefficients. Do not determine the…

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Q: Which differential equation follows the form A (x) dx +B(y) dy=0? A B dy dx dy - y --2y=0 - 2dx=0…

A:

Q: Find all values of k for which the function y = sin(kt) satisfies the differential equation y" + 8y…

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Q: Determine the values of r for which the differential equ y" - y = 0 has solutions of the form y =…

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Q: 5. Given the integral expression below: T/2 (8 + 4 cosx) dx Evaluate its value, a. analytically b.…

A: This is a problem of Numerical Analysis.

Q: Need this in complete and handwritten solution, thank you! 3. Solve for the Homogenous Differential…

A: Ode

Q: Solve the following differential equation Integrating Factor by Inspection: 1. (x4+y4)dx+xy3dy=0

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Q: 3 2 Evaluate the integral| (4- y?) dy dx. 0 0 The value is (Type a simplified fraction.)

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Q: xy'+2y = x² y(2)= %3D %3D 914

A: In this question we will use basic of calculus i.e solution of differential equation of type…

Q: tind the particular solution of the differential (0?+ 4D +3)x given that t- 0, and dx -2 %3D

A: Given differential equation is : D2+4D+3x=e-3t At t=0, x=12 Att=0 ,dxdt=-2

Q: 1. The exact differential d(xy)= xdy+ ydx, what is the d( = 4x' y'dy+2xyʻdx. 2. The exact…

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Q: ve the separable differential e C 1 = x² + t d find the particular solution sa 0) = = - 2.

A: topic;- application of integration

Q: 2. Find the general solution to each of the following DEs, showing work- ing dy (a) -x = xe dx dy…

A:

Q: A) Classify the following differential equations and solve it : 1- Y = (1 + e*)(y² – 1) dy (using…

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Q: mzer Mathematics Q1 Solve the following differential equations dy +y = y°x² In x dx dy (sinx – siny)…

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Q: 2=2y +z and dx dz = 3y satisfies the relation dx Let k be real constant. The solution of the…

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Q: 2x Given: z = xlny - = + y sinh√x O O O - - 2x+11n4 y³ - 2x+1 In²2 y3 2x+1 in ²2 y³ 1 2x+2 In2 y3…

A:

Q: A. Solve the following differential equations using the method indicated. 1. xy'dx + ex*dy = 0 2.…

A: Given:xy3dx+ex2dy=0

Q: Given that a and b are positive constants with a < b. Show how you find the antiderivative and use…

A:

Q: Solve the following differential equation Integrating Factor by Inspection: 1.…

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

Q: A. Obtain the roots and the factored operator form linear differential equations y = x? – 5 sin 3x y…

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Q: iven that a and b are positive constants with a < b. how how you find the antiderivative and use the…

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Q: 17. Given that x=e" and y= 3t find dy in terms of x. dx 18. Differentiate X-3 +2ln( with respect to…

A: Differentiate wrt x

Q: y (x² + y² – 1)dx + x(x² + y² + 1)dy = 0 %3D

A: Given the differential equation y is not exact.

Q: The function cosh(2x) is a solution of the differential equation O (A) y" + 4y = 0 O (B) 4y? - (y')?…

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Q: Solve the following differential equation Integrating Factor by Inspection: 1. xdx+ydy=(x2+y2)dx

A: Given: xdx+ydy=(x2+y2)dx

Q: Q/ Find the deneral solution tb the differential eguation ( o-V= 1+x

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Q: Determine the absolute value of "k" so the given the differential equation below is exact. (y3 +…

A: The given differential equation is: y3+kxy4-2x dx+3xy2-20x2y3 dy=0

Q: 8. Solve the initial-value problem y" – y = cosh r, y(0) = 2, y'(0) = 8 %3D

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Q: 4) Check to see if the following differential equations are exact. If so, solve it. If not, find the…

A: The given differential equation is…

Q: Find the differential equation y(x – 1)dx – (x² – 2x – 2y)dy = 0 a.x? + 2x + 4 = 2Cy? b.x? + 2x + 4y…

A: First we find the integrating factor then the differential function which is the solution of the…

Q: Q: Solve the following differential equations: 1. {[1+y²]sin(xy) + xycos(xy)} dx + {[1+x²] cos(xy) –…

A: Given The given differential equation is 1+y2sinxy+xycosxydx+1+x2cosxy-xysinxydy=0