Reduce the following differential equation to first-order and solveit. ww www 1-x2y"-2xy'+2y=0;y1=x

Q: Find the differential of the function. y = e³x dy = =

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Q: 4. y(4) + 17y" + 72 = 0.

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Q: +QA = 0 ab ac ad

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Q: Solve the differential equation: 2 1 x²y'' 2y Xx -

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Q: Example: Solve the DE y" – (1+ x)y = 0

A: See the attachment.

Q: -4지 (2) %3D y(e) %3D

A: The given differential equation is y'=-4xy,y(2)=3 dydx=-4xyydy=-4xdx integrating both sides

Q: x*y' Vy +3xy =10x²

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Q: Q2. Factor out the differential equation and find the general solution. xy" +(2x-1)y' +(1-3x)y=0.

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Q: 5. e-ta s²+28+7 { = ?

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Q: 3. t²dy = (8ln²t – ty)dt

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Q: Solve and Explain the summary of steps followed while solving the differential equation. (3y" + y' –…

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Q: 4. xt' + t = xt³

A: Given differential equation is, xt'+t=xt3. . . . (1) Rearranging the equation -xt3+xt'+t=0 Let us…

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Q: dzy d + 3- 4y = x? B: Solve the differential equation:

A: Given: d2ydx2+3dydx-4y=x2...(1) So, we can also write as: D2+3D-4y=x2 So, the auxiliary equation is:…

Q: 1. y-14y- 48y = 0 2. y'-12y + 27y = 0

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Q: Evaluate the Differential Equation by Integrating factor. Solve: xy' = 3y + x^4_y(1)=7 Find the…

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Q: the appropriate that should be applied the differential equation 4 - 54 - 5 xyở ³ 2 K

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Q: Solve the following differential equation. y + y +y=x²-2x

A: We have to solve the given differential equation.

Q: Find a differential equation whose general solution is 8t y = c₁est + c₂e-2t. = 0

A: We can find the differential equation as below.

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Q: 2. y + xy = 6x/y %3D

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Q: Solve the following differential equation. y"+y' - 2y = 0

A: Given:The given differential equation is .To Find:We have to solve the given differential equation.

Q: Solve the following differential equation y"x+ 3xy' - 3y = 0

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Q: 7. ON te 2.

A: We have to solve

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.