8) Solve the differential equation y"+y=sinx. First find the complementary solutio then find the particular solution by using the method of Variation of Parameters. With yı y2 W y2 |yi y½[' W1 |f(x) y½| W2 calculate W2 uz W1 u = W W Integrate u', u, and set yp=uY,+u,Y, State the solution y=y,+y,

Q: y" +y' – 2y = 4e* – 2x

A: We have the given differential equation is y''+y'-2y=4e-x-2x2     …..(1) The auxiliary equation for…

Q: Consider the Bernoulli equation y' + -y = 3y°. After applying an appropriate substitut this equation…

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Q: x' = (C )x ´sec X + 0, 1

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Q: xy2 y' = ey + sin y dy = dx x+y y' = x2

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Q: - y" 3y'+2y=- 1+ e-x Use Variation of Parameters. Do not simplify final result.

A: Step 1: Step 2: Step 3: Step 4:

Q: Use variation of parameters to find a particular solution, given the solutions y 1, 2 of the…

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Q: y" + 3y' + 2y = cos(e).

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Q: I Solve the differential eauations 4. (D7D+19D+13)y =0 when x-0, y=0, y'=2, y"= -12, find y()

A: Given differential equation is D3+7D2+19D+13y=0 and given when x=0, y=0, y'=2, y''=−12 that is y0=0,…

Q: ng the method of undetermined coefficients, find the particular solution y, for the NHLDE Y'"-…

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Q: Use variation of parameters to find a particular solution of the DE y/" – 4y + 4y then write down…

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Q: kpression for "12 times x."

A: Times means multiplication. Sometimes it is denoted by dot.

Q: Find general solution of y" – 2y' + y = , By Variation of t2+1' parameter method.

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Q: Find the general solution of the equation by the variation of parameters method: y" – 2y'+ y = æ 2e"

A: We use the procedure of method of variation of parameters.

Q: y" – 2y' + y = –3 – x + x²,

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Q: 2. Differentiate the following equations. a. Differentiate. 11 y 1=22²2²² 7x²

A: Since we are given with the multiple  number of subpart  question answer will be according to the…

Q: 3 Parameterize y(x) = +1 using x = t sin x Ans=

A: The answer is: y(t) = (-3/sin(-3/sinx) + 1)) + 1Explanation:To answer this question, you just have…

Q: Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the…

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Q: Q4. Simplify the following expression: 3-5 x 39 Click on image to enlarge if needed 12 81 243 324

A: To evaluate :- 3-5 * 39

Q: (2xy¹e³ + 2xy³ + y) dx + (x²y²e³ − x²y² − 3x)dy = 0

A:

Q: 3. Find the general solution of y" – 3y' + 2y = e" using the method of variation of parameters.

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Q: Bernoulli Equation (17) y'+ () y = x³y³ (18) y' + 3x²y = 4x²y² (19) (x²yª – 1)dx + x³y³dy = 0 (20)…

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Q: 2. Find the general solution for Differential Equation: (x² - 1)y³dx + x² dy = 0

A: Given : x2-1y3dx+x2dy=0 To Find : General Solution of differential equation

Q: Consider the equation below: u’=u2 – (7/x)u + 8/x2; u=-y’/y Obtain the linear second order…

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Q: IV. y-y=sin x+cos 2x +e

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Q: y" + y = sec (x)

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Q: Fill in the blank The equilibrium solution(s) of y' = 3y(1–where k > 0 are %3D he difference y',…

A: Equilibrium solutions for a differential equation are given by  y'=0 Also wronskian of two solutions…

Q: Find the solution. (D³ +7D2 + 19D + 13)y =0; when x =0, y=0. y' =2, y"=-12 A y = e-2'sin3x B y =…

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Q: Find the particular solution: d³y d²y +2 = dx3 dx² 0 when x = 0, y = -3, y' = 0, y = 12

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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.