Cônsider thé föllówing initial-value problem. 4x2y" + y = 0, y(-1) = 4, y'(-1) = 2 Use the substitution t = -x and find general solution of the resulting differential equation. y(t) = Solve the given initial-value problem. y(x) = 4Vx (iln(x) - i+n) ,X < 0 %3D

Q: Q2/ Solve the following differential equation :- x?y" – 2xy' + 2y = xlnx, y(1) = 1: y'(1) = 0

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Q: 9 Find the general solution to the differential equation y' where x > 0. y = +C

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Q: Q2: solve the differential equation x²y' = y² + xy + x² subjected to the condition y(1)=1 and give…

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Q: You and your friends started industrial training in one of Megah Holding's branch last month. A…

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Q: Q5: Solve the differential equation y' y = 1 Subjected to the condition y(1)=e-1

A: we have to solve differential equation

Q: 2 4 Solve the differential equation y dx - 2(y - x) dy = 0. If y = 1 when x = 3, determine x when y…

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Q: Find the general solution to the separable differential equation: (2x + 1)(x + 1)y' = - %3D For full…

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Q: Use Adam-Moulton three step implicit method for the following differential equation to correct the…

A: The Adam-Moulton formula: and

Q: V1- (-1)*x²dy = (1+(–1)“y³)dx

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Q: 6. Find the differential equation whose general solution is y=C₁X + Czex, b. a. (x-1) y"-xy' +y=0…

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Q: (1) If Q(t) is the amount of oil in the water t days after the leak was capped, the differential…

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Q: Find a general solution for y'+ (1/x)y = 0, for x > 0. To receive any credit, you must use the…

A: To Find a general solution for y'+ (1/x)y = 0, for x &gt; 0. We use the method of seperation of…

Q: (y-2) dx - (x x-y-1 _y' = 3v-3x -

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Q: Solve for the exact first order differential equation. Find the appropriate integrating factor and…

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Q: 4 Given that y = ex solves (x+1)y"+xy-y=0 find the second solution of the above differential…

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Q: Solve the differential equation by separation of variables. Show your complete solution. 1. (x+2)y =…

A: This question is based on differential equation solution.

Q: 3x + y + z = 0; z(0) = −1

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Q: Find general solution of the differential equation y" +10y' +25y = 0.

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Q: You are given the following differential equation:  dy/dx = y2 (1-8x) if y > 0  Which method for…

A: If the differential equation is of the form dydx=f(x)g(y). The equation is solve using the variable…

Q: 7. Solve the differential equation h'(t)=8t³ +5, h(1)=-4.

A: solve differential equation h't=8t3+5, h1=-4

Q: The indicated function y,(x) is a solution of the given differential equation. Use reduction of…

A: We will use the reduction formula to find the other solution, y2

Q: Solve the following a. y' - 5y = e5x; b. y’ + y = xe-* ; c. y' + 4y = 2 cost; y(0) = 4 differential…

A: a. We have to solve the given differential equation.

Q: Q/Find the general Solution to the differential equation Using the transaction method is not…

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Q: y' - 2x = -e-t; y(0) = 2

A: y' - 2y = - e-t, y(0) = 2 Thia is a linear differential equation of first order  Integrating factor…

Q: Q4: Solve the given differential equation by finding y' only 6y" y² = = (3(y')² + 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.