Given the first order differential equation, select all three correct answers: dy - ху3 - ху dx DA. The given equation is linear. O B. An implict general solution is given by: 2(1+c ex) = 1, where c is a constant. OC. An implict general solution is given by: y2(1+ce-x = 1, where c is a constant OD. The given equation is Bernoulli. DE. The given equation is separable. OF. The given equation is exact.

Q: State the order of homogeneity and solve the differential equation as a homogeneous equation. x dy…

A: See the attachment

Q: Solve the following differential equations: (D² – 4D + 4)y = x³e2x %3D -

A: Consider the given information: The given differential equation is, D2-4D+4y=x3e2x

Q: Solve the given differential equation. dy = 18-ay %3! dx O y= (6x22 -C) O y = 6x2 + C O y = 6x + x2…

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Q: A cup of hot coffee initially at 95°C cools to 80°C in 6 min while sitting in a room of temperature…

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Q: Given the solution to a differential equation, determine the corresponding roots. y = C₁ + C₂x +…

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Q: (4D58D4 17D³ + 12D² +9D)y = 0 -

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Q: Given the equation 2xsin² ydx-(x² +10) cos ydy = 0, Find an implicit solution. Find the constant…

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Q: Q2: Solve by Separable Differential Equation. y=xe

A: We need to solve the separablefydx=fxdx differential equation

Q: Given the function y₁ = x² is a solution to the differential equation x²y" - 3xy' + 4y = 0, find a…

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Q: b. 6y²dx – x(2x³ + y)dy = 0 -

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Q: Given the differential equation: D°(sin x- cos x+ 3e* +x²) What is the final derivative in the given…

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Q: Using an operator , solve the following differential equations d2y/dx2- 10dy/dx + 25y= 0

A: This question is based on solution of differential equation using D operator.

Q: For the differential equation given below, variable. d²x dr2 + kx=Acost is the independent variable…

A: Given :d2xdt2+kx=Acost

Q: Solve the differential equation. Show your complete and clean solutions. (x-2y+5) dx - [2(x-2y)+9]…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: У - 2у+ %3D 1+ x

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Q: (2xy + x² + x*)dx – (1+ x²)dy = 0

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Q: Use an appropriate substitution to solve the equation 9. and find the solution that satisfies y(1) =…

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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.