y' + 2y = x'e-2*, y(0) = 1

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

A: Given, A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. pumped into the…

Q: dy Q3. Solve the DE da +y - y? provided that y1 = - is one known solution of the equation.

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Q: Find value of the NEGATIVE root for: a = 4.7 and b = 4.6 and c = -4.1. Give your answer to 3 decimal…

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Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: Q1. Solve the following dy (a). y² + xy³ + (5y² – xy+ y³ sin y) = 0. dx

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Q: Date (2) (3 x² + y cusx) dx + (sin x - 4y³) dy so solve using exact equations X = 0 y = 2 Answer: 0=…

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Q: Determine the value of k that will make the equation exact and solve the resulting differential…

A: Solution :-

Q: (6): Partial Differential Equation Solve the following equation do/dt-h² d'o/dx²2 0 (x, t) LC t=0…

A: We have, the given partial differential equationThe solution for partial differential equation with…

Q: verify that to the and find the function Y = C₁x + C₂ x 2 1 (₂ x ² is a differential equation: x³y"…

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Q: solve the differential equation: (3y ′′ + y ′ − 14) = 24e^16 − 48 (Explain the summary of steps…

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Q: 4. sinx-siny dy + cos x-cosy dy The ㅠ X = 6 = T|Y प = 0

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Q: 4x²yy' 3x(3y2 + 2) + 2(3y +2)3 %3D

A: Given differential equation is 4x2yy'=3x(3y2+2)+2(3y2+2)3 where y'=dydx We have to find the solution…

Q: differential equations. dy = dr(²yz²+72²)

A: The given differential equation is dy=dx2yx2+7x3x3. We have to find the solution of the differential…

Q: 9. (x + x* + 2x²y² + y4)dx +y dy = 0; when x = 1,y = 1

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Q: -ka dt2 Sdlve the differential equation and express the X func tion of trieonometrie func tion as

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Q: Solve the separable differential equation 7e-3x+2x -xcosx y' = -6y3

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Q: Solve the ordinary differential equation 4x²y"+(1-2x)y = 0, Then evaluate the first four terms of…

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Q: Solve the differential equation dy dr e-"(1 - y)? in general. Then sketch solution trajectories…

A: For the solution follow the next steps.

Q: Question 3 : 2y!ly y" +2)=xy'k

A: As per the question we have the following first order exact differential equation : 2y'(y11 + 2) =…

Q: 6. (y cos x + 2xev)dx + (sin x + x²e° + 2)dy = 0; when x = 0, y = 0

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Q: Q1:- Solve the following DEs:- (-4y + e-3*)dx = 4 dy %3D

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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.