1. x In x sec² y dy + [tan y – (In x)°]dx = 0 When:x = 1; y =

Q: Find the value of the constant k so that the differential equation (6xy³ + cos y)dx + (kx²y² − x sin…

A: For the given Exact Differential (6xy3+cosy)dx+(kx2y2-xsiny)dy=0 value of k is 9 Hence option (A) is…

Q: Find the particular solutions of the given differential equation dy dz 2 cos a sin a given y = 1…

A: 1. Sin(2A)=2sin(A)cos(A). 2. Sin²A+Cos²A=1.

Q: 3. Find the general solution of this separable differential equation. dy y cos x dx sin x + 2

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Q: y1 is a solution to the given differential equation.Use the method of reduction of order to…

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Q: 3. (a). Show that the differential equation below is exact. Hence, determine its implicit solution.…

A: as per our guidelines we can provide answer to one question at a time  , you can repost others

Q: 2. Solve the ordinary differential equation. a) e2*cos(y)sin(x)dx + e*tan(y)dy = 0 b) (x* + 1)dx -…

A: To solve the following problem we use the seperation of variable method and also use  standard…

Q: If a nonhomogeneous linear differential equation has g (a) = sin 5a, what is the form of its…

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A: Find the second derivative and substitute in the given differential equation and solve for r.

Q: 2. Solve the following Exact Differential Equation with boundary value y(1) = 1 (x + y)²dx + (2xy +…

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Q: The value of the constant a such that the given differential equation is exact ) 1 1 dx + 1 dy = 0…

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Q: 7. 1 (x dy – y dx) = 0 x² + y?

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Q: Solve the differential equation below over the interval from x = 0 to 1 using a step siz of 0.2…

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Q: 1. Consider the differential equation: dy = = 2y - cos (3t) dt a. Find the homogeneous and…

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Q: 1. A solution for the differential equation is y = e"x A, sin (vx) + A, cos (vx), where m and n are…

A: Let's find.

Q: b) Find the general solution of the following homogeneous differential equation. dx х - + tan– y = -…

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Q: - Obtain a numerical solution of the differential equation = y - 2x in dx the rang 1.0(0.2) 2.0,…

A: To find the solution of the first order differential equation dydx=fx,y with the initial condition…

Q: Consider the differential equation: 1. y"-y%D What is the general solution? y= [a + In(1 +te *)]e* +…

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Q: Solve for the value of “C” on the given differential equation below. Let y(1)=1 y’=x-2y

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Q: 6. a. Solve the differential equation below under the following initial conditions: y (0.5), y (1.0)…

A: Since you have posted a multiple question according to guildlines I will solve first question(a) for…

Q: 1. A solution for the differential equation is y = e"* A, sin (vx) + A2 cos (vx) , where m and n are…

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Q: (b) Consider the differential equation ydx + x(lnx-lny - 1)dy = 0. Hence, or otherwise, use an…

A: Let us consider a differential equation of the form Mdx+Ndy=0 To equation is exact if ∂M∂y=∂N∂x then…

Q: Given the differential equation За" +2 find the particular solution, y = f(x), dx with the initial…

A: Given,        The differential equation dydx=3x2+2y and y=x with the initial condition f-1=6.

Q: Solve the given differential equation subject to the indicated conditions. y" - 4y = x + sin x, y(0)…

A: The given differential equation is y''-4y=x+sin x, y0=5, y'0=2y

Q: 1. Find the particular solution of the differential equation that satisfies the initial conditions.…

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Q: The solution of the separable differential equation – x²y² = x² is: dx None of the above…

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Q: 4. Solve for the general solution of the differential equation using homogenous equatiorn [x cos?…

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Q: (y cosx+2.xe" ) dx +(sin x + x°e' -1)dy = 0

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Q: Solve for the value of "C" on the given differential equation below. Let y(1)=1 10 ( x³ + y) dx -…

A: Given differential equation x5+ydx−xdy=0 We have to find the value of C and the general solution of…

Q: a. b. algal dy dx dy dx + y = xy³ - y = ex y² -X

A: See this solution in below.

Q: Let y be a solution of the differential equation * + (1+ )y = !, where x > 0 such that y(1) = 1+2.…

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Q: Show that y = 1 - x cot x + A cosec x, where A is a constant, is a general solution of the…

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Q: Solve the seperable differential equation for. dy 1+ x -; x > 0 xy10 da Use the following initial…

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Q: 0 to 1 using a step size Solve the differential equation below over the interval from x = of 0.2…

A: This is a problem of Numerical Analysis.

Q: For the differential equation y' + 4y = 0, a general solution is of the form y = C, sin 2x + C2 cos…

A: Given initial value  problem y"+4y=0    , y(0)=-2 , y'(0)=-10 y=c1 sin2x  +c2 cos2x

Q: Find the solution of the differential equation y' cos x 0. sin x a. y = cos x + C sin x b. y = cos x…

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Q: 7. Find a linear differential equation with constant coefficients Ly = 0 such that y(x) = cos(x) +…

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Q: b) Show that the following differential equation is exact. Then, find the general and particular…

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Q: Consider the differential equation (DE) .7 dx2 +3 + y = sinh x + 2" a) Its i) order is ii) degree is…

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Q: Solve for the value of "C" on the given differential equation below. Let y( 0 )=1 2( 2xy +4y -3 )dx…

A: We have to solve given differential equation:

Q: Given the differential equation: dy y +1 = − dx X with initial conditions y = 1 at x = 2.0, produce…

A: Given the differential equation: dydx+1=-yx with initial condition y=1, x=2 To find a numerical…

Q: Determine the special solution of the ordinary differential equation of order 1 below and describe…

A: Given: 4 d^2y/dx^2-(4*5)dy/dx-(3*5)y=0, y(0) =1,y'(0)=5

Q: Solve for the particular solution of the given differential equation. Final answer can be expressed…

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Q: Solve the separable differential equation dy -0.1 dx cos(y) and find the particular solution…

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Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli…

A: The given DE is: xdydx+y=1y2⇒y2dydx+y3x=1x...(1) Now, substitute y3=u⇒3y2dydx=dudx⇒y2dydx=13dudx

Q: The solution of the following separable differential equation x²y-y ア=リーン y' with y(3) = -1 is y+1…

A: Given,          y'=x2y-yy+1 with y3=-1

Q: Consider the differential equation: y" + y = sec x,0 <x <n/2 What is the particular solution y.? Yp…

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Q: (d) y' = x(1 + y²), y=tan(\x²)

A: Solution of the differential equation satisfy  the differential equation

Q: Find the general solution of the following ordinary differential equation (x-2y-3)dx+ (2x + y-1)dy…

A: Consider the given differential equation: 2x+tanydx+x-x2 tanydy=0 Here, the objective is to find the…

Q: 3. Determine whether the given differential equation is exact. If it is exact, solve it. e (x – y3 +…

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Q: 1. a) A non-linear ordinary differential equation is given as: dy (cos* x) + y (sin x) (cos³ x) – y³…

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