dx 5. x + 1²x sin t %3D dt

Q: Solve the differential equation. (Use C for any needed constant. Your response should be in the form…

A: The given differential equation is: xy2y'=x+4   We know that' The Power rule: ∫xndx=xn+1n+1+C And…

Q: Q1. What is the condition for a differential equation to be exact? Determine whether the given…

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Q: Which differential equation when multiplied with y " the resulting differential equation is exact? A…

A: A  2y-3xdx+xdy=0B  x-y2dx+2xydy=0C  2xy2+ydx-xdy=0 Mdx+Ndy=0∂M∂y=∂N∂x

Q: Given an ordinary differential equation dy dx dx (a) Show that the equation above is separable. (b)…

A: We will find out general solution.

Q: 2. (2x + 3y' )dx + 9xy'dy = 0

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Q: Q 1. (a) Define order and degree of differential equations with examples. Solve, (1+ y?)dx = (tan-ly…

A: Order of a differential equation- Order is defined as the highest derivative in  the differential…

Q: 2. Solve the given differential equation by variation of parameters. (Recall: csc x = T cos? x +…

A: Given,        y''+y=csc(x)                     ...(1)

Q: II. Find the differential equation by eliminating the arbitrary constant/s. 1. y-¹ = x(3e* + c) 2. y…

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Q: dy x*y dx sec x

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Q: Q.2-Solve the differential equation (answer three dy а. (Зух? y (3yx² -) + (x³ + cosy +-). x2 dx

A: Introduction: A first-order differential equation is standardized as  Mx,ydx+Nx,ydy=0 If ∂M∂y=∂N∂x…

Q: 十3 r 十2dr=G

A: The differential equation is given as , ydy+3y2xdx+2x3dx=0 find the solution.

Q: d'y Solve the Differential Equation dx? -9y = 3sin 22 cos x. %3D

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Q: 1. Solve the differential equation. Explain your steps in detail. dy 5y = e -2x

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Q: 3.(Straightforward) Determine if each of these differential equations is exact, and if so, solve it.…

A: As per our guidelines we are supposed to answer only one question i.e. the question no 3)a). For the…

Q: Q-3 Find the the general solution of the differential equation (D? + 25)y = csc x sin x + sin 5x cos…

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Q: Solve the given differential equation. Find an implicit solution. Use c for the constant of…

A: We have to solve given problem:

Q: Ax+1 Given, (- +) dx + ( ) dy = 0 is an exact differential equation. %3D y5 Determine the value of…

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Q: 1. (x – 3)dx + 4(x +y- 1)dy = 0

A: Follow the process of differential equations below. Remember to undo the substitution at the end.…

Q: dy - y = 3e*y' dx . Solve the Bernoulli differential equation

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Q: (y? cos x – 3x2y – 2x )dx + (2y sin x – x² + Iny )dy = 0

A: is theGiven :(y2cosx-3x2-2x)dx+(2ysinx-x2+lny)dy=0Check the differential equaiton is exact, if the…

Q: solve the differential equation:  (dy/dx) + (e^(1+x)) =

A: Apply separation of variable method

Q: C1. (a) Solve the nonlinear differential equation x'y-x = v" cos x dx %3D

A: That's easy. Have a great day!!!

Q: d'0 Solve the differential equation dx² do =1 and 0(0)= 7. dx 2 = 15x +, with the conditions 3

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Q: Determine whether given differential equation is exact. If it is, find the solution. (sin 0 – 2r…

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Q: Q|Solve the differential equation by linear method dy 4 -2(r +1)³= dx %3D (x+1)"

A: As per our guidelines, I am solving only the first question, please resubmit other questions.

Q: dy Solve the differential equation = 6.x– 2y by using the substitution u = Ax+ By+C. dx Solve the…

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Q: Solve the given differential equation by separation of variables. dx + e4xdy = 0

A: The given differential equation,dx+e4xdy=0

Q: solve the given differential equation. dy/dx = y/x ln x

A: Given that, dy/dx = y/x ln x Applying variable separable method. Firstly applying separation of…

Q: %3D Find the general solution to the differential equation: y' = ( +e*) [5 tan(x)]

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Q: y" - y = x?ex Solve the following differential equation

A: 1f(D)eax V =eax1f(D+a)V

Q: Solve the differential equation with appropriate method. Simplify final answer the simplest possible…

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Q: 3. (2xy – vldx + x(x + 1)dv

A: Solution of the problem as follows

Q: dy し56 sec? (x") (x *) dx ×2 - る× (x-3)2

A: Consider the first order differential equation  We can solve these differential equations using the…

Q: Check whether the following differential equation is exact. (6ye-3z + 3x)dx + (5y – 2e3")dy = 0 Then…

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Q: solve the differential equation x dy/dx - y = 2x2 and find the particular solution when y(1)=5

A: given differential equation xdydx-y=2x2  with conditions y1=5 claim- to find the particular solution

Q: Q-25 [ Show that the given differential equation is not exact hence solve it xʻydx – (x + y')dy = 0

A: Exact equation:  The necessary and sufficient condition that M dx +N dy =0  be exact  is ∂M∂y =∂N∂x…

Q: Solve the given differential equation by separation of variables. dx + e2xdy = 0

A: Given: dx +e2xdy = 0 To solve: The given differential equation by separation of variables.

Q: dy Solve the differential equation: dx tan? (x). The curve passes through point (0, 0).

A:

Q: Exercisel: Form the differential equation by eliminating arbitrary constants: 1- y? = Ax + B 2 - y =…

A: 1.

Q: (x+2)? x² -4 dy 2y dx x? -4

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Q: dy 7. dx cos(x + y), when x = 0, y = %3D %3D 4

A: Follow the procedure given below.

Q: dy 3 +-y= dx cosx B. Solve the differential equation

A: The solution is given below

Q: use the exacr differentials to solve the differential equation. ydx + (x + x³y²)dy=0

A: The given differential equation is: y dx +x+x3y2dy=0 Result: A differential equation Mdx+Ndy is said…

Q: dy Solve the differential equation %3D dx

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Q: Ar+1 Given, (- +) dx + ( ) dy =i® an exact differential equation. Determine the value of A.

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Q: d²y dx² dy dx -+ 2y = cos (e-x)

A: The given differential equation is;  d2y/dx2-3dy/dx+2y=cos(e-x).

Q: Solve the differential equation dy +23 x > 0. dr

A: The give equation is a first order Bernoulli ODE of the form: A first order Bernoulli ODE has the…

Q: solve the given differential equation on the interval x > 0. [Remember to put the equation in…

A: First determine the complementary function CF for the differential equation.…

Q: 03/ Solve the differential equation. dy + x³y = - sec (xy) dx

A: