Answer the following using Homogenous ODE in Differential Equation. 3(3x2 + y?)dx – 2xydy = 0

Q: 2. Solve the following differential equation in two ways: once using separation of variables, and…

A: Here we have to use variable separable method and reverse product rule to solve the differential…

Q: Solve the following homogenous ordinary differential equation: (y + x) dy (y – x) dx

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Q: Answer the following using Homogenous ODE in Differential Equation. [x csc( c() - y] dx + xdy = 0

A: we have to solve the following homogeneous ode

Q: Prove the following Homogenous Equation in Differential Equation. 3(3x2 + y?)dx – 2xydy → x³ = C(9x²…

A: Compare with exact differential equation and then solve

Q: Prove the following Homogenous Equation in Differential Equation. [x csc (-) – y] dx + xdy = 0 →1n=)…

A: Given differential equationxcscyx-ydx + xdy = 0We prove that lnxc = cosyx

Q: 6.) (y In xy + 3x²) dx + x In xy dy = 0

A: First we need to simplify the given equation then solve it by standard formula. Following formulas…

Q: Solve the following differential equation x²y" + xy' + y = cos(Inx)

A: Cauchy Euler's differential equation

Q: Solve the following differential equation: (3x°y+2xy)dx+(x'+x +2y)dy 0

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Q: 4. Solve the following differential equation: dy dx sin x + y cos x = sin x cos x

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Q: An appropriate integrating factor µ(x) for the following differential equation (2y² + 3x)x+ 2xydy=0…

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Q: The following differential equation is an ordinary differential equation O True O False dx

A: We have to says that the given statement i.e. the differential equation ∂y∂x=xt-yt+1 is an ordinary…

Q: Solve the following homogenous ordinary differential equation: dy (у + x)- 3D (у — х) dx

A: We have to solve homogeneous ordinary differential equation.

Q: Answer the following using Homogenous ODE in Differential Equation. 3xydx + (x² + y²)dy = 0

A: Hint: By putting y=vx we can solve homogeneous differential equation.

Q: 2xydx – V x² + y²dy = 0

A: The solution is given as

Q: Solve the following differential equation using appropriate method. 2. (2x + 4y + 6) dx + (4x -2y-5)…

A: The given differential equation is; (2x+4y+6)dx+(4x-2y-5)dy=0

Q: Solve the following differential equation by using integrating factors. xy' = 4y – 5x? |

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Q: Reduce the following differential equation to first-order and solve it. (1 – x2)y" – 2xy' + 2y = 0 ;…

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Q: 3ely)dx +3e dy = 0 y

A: In this question, the concept of a Differential equation is applied. Differential Equation A…

Q: Consider the following differential equation f + = cos (x) What is the general solution ?

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Q: Solve the following differential equation using appropriate method. 5. (2xy- 3x?) dx + ( x² + y) dy…

A: Given (2xy-3x2)dx+(x2+y)dy=0

Q: Check the exactness of the following differential equation and find its solution: {2xy cos x² - 2xy…

A: Exact differential equation

Q: Which of the following will be an integrating factor for the differential equation dx

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Q: Find the particular integral of the following ordinary differential equation d2y/dx2 +9y =cos3x.

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Q: Answer the following using Variable Separable in Differential Equation. dr = b(cos0dr + rsin0d0)

A: Given    dr=bcosθ dr+r sinθ dθTo find  Solve the given separable differential equation

Q: tr dr dt +x³ tcost

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Q: Consider the following differential equation. (x - y + y² sin(x)) dx = (6xy5 + 2y cos(x)) dy

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Q: 3. Select the correct type for the following differential equation (2xy + 3y²) – (2xy + x²)y' = 0

A: The given differential equation is: (2xy+3y2)-(2xy+x2)y'=0(2xy+3y2)dx-(2xy+x2)dy=0Here, M=2xy+3y2 ;…

Q: Solve the following differential equation: (3x y+2xy)dx+(x' +x +2y)dy 0

A: (3x2y+2xy)dx+(x3+x2+2y)dy=0

Q: y = C1 e2x c cos 3x + c2 e2* sin 3x

A: The general solution is given as , y=c1e2xcos3x+c2e2xsin3x find differential equation.

Q: Solve the following Differential Equation using variable separable. ylnx lnydx +  dy  = 0

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Q: Solve the following differential equation by using integrating factors. You may assume that * > (x +…

A: To solve the given differential equation.

Q: Solve the following differential equations by finding integrating factor dy --y = e2x dx

A: We need to solve the given differential equation using integrating factor method.

Q: Consider the following differential equation. ydx - 7(x + y) dy = 0

A: Given differential equation is ydx-7x+y9dy=0. To find: 1. Coefficient function Py. 2. Integrating…

Q: I. Solve the following manually using separable differential equations method. dy 2y 1.- dx

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Q: For what value of k is the differential equation (k²y-6x)dx+(2x² + 2y)dy=0 exact? 2

A: Given that: (kx2y-6x)dx+(2x3+2y)dy=0   NOTE: As per our answering guidelines, we can only answer 1…

Q: 4rdx + (21*y +Зу)dy 3 0.

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Q: Solve the following differential equation xy' +3y= - (x'tanx) y Select one:

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Q: dy 3. + y = ry° dr

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Q: Find the salution of the following differential equationss © ý=ytanh(x)

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

Q: Which of the following is a solution of the differential equation dy/dx-4xy=0?

A: given dydx-4xy=0

Q: Given the following ordinary differential equation y' = 5y What is a solution for y(x) such that it…

A: Solve the given ODE by separation of variables.

Q: 1) (x+y)dx+xy dy-0 ans:

A:

Q: Classify the following differential equation as linear or non-linear. (x2 - 2y) ((dx)/(dy)3) - (y3 +…

A: Given: The Differential equation is x2-2ydxdy3+y3-5d2xdy22=-16.

Q: dy dr 3 = e*y*

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Q: Solve the following differential equation: fii(x)=4x3+3x2+2x+1 with fi(0)=2 and f(0)=1

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Q: Solve the following differential equation by using integrating factors. a*y' = xy - 8hn a, y(1) ||

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Q: The following differential equation can be solved by assuming dy y² + x²dy dæ dx

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Q: Solve the following differential equation sec3x dt = tan2 t dx when x = 3π/2 , t = π/4

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.