2. Solve the equation using Variation of Parameters: y" – 5y' + 4y = x .

Q: Obtain the solution using Integrating Factors Found by Formulas 1. 2(2y² + 5xy - 2y + 4)dx + x(2x +…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y' = y2/√x and y(1) = -1.  What is the exact…

A: In the given question, it is asked to solve a differential equation using Euler’s method.

Q: 3. Solve the following equation using the determination of integrating factors. 1. y(2x – y + 1)dx +…

A:

Q: 2. Solve the ff. equation using integrating factor. dy 2y – e3r dx

A: Given: dydx=2y-e3x

Q: 3. Obtain the homogeneous linear equation satisfied by the following function. y = x² Sinx + e5x

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Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: Solve dy/dx =( y+x-2) /(y-x-4) Equation s reducible to homogenous form

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Q: Find the general solution for -x) dx - (-y) dy dy = 0

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Q: Solve the differential equation using Variation of Parameters e* (D² – 2D + 1) y

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Q: Use the Euler method with dx = 1/3 to estimate y(2) if y' = y - e2xand y(0) =1.  What is the exact…

A:

Q: Solve the differential equation by variation of parameters. 4y"8y' + 8y = ex sec x y(x) =

A:

Q: Q3 (d^2 y)/(dx^2) - 2dy/dx of Undetermined Coefficient) 20e^(-x) cos(x), y(0) = 0 = y'(0) (Use…

A: we have to solve given differential equation by using method of undetermined coefficient

Q: 2, t'y"+ty'+y= Cos(int)

A:

Q: Find the differential dy of the given function. Y = 5x+(sin(x))^2 Dy=?

A: Topic- differentiation

Q: Find the solution asked using the process of Homogeneous. (16x + 5y)dx + (3x + y)dy = 0; the curve…

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Q: (2х — Зу)dx + (2у — Зx)dy %3D 0

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Q: 4. Solve the equation using homogeneous equation (x– 2y)dx+(2x+ y)dy = 0.

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Q: Use Variation of Parameters to find a particular solution to the non-homogeneous equation y′′−2y′+y=…

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Q: Solve the given third-order differential equation by variation of parameters. y"+ 64y' = sec(8x) |3|…

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Q: (1+ 2e*/»)dx + 2e*ly (1–) dy = 0

A: Given the differential equation as (1+2ex/y)dx +2ex/y1-xydy = 0 It can be rewritten as (1+2ex/y)dx =…

Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

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Q: Obtain the general solution using variation of parameters (D²+3D+2)y=cos(e^-x)

A: We have to solve the given differential equation by variation of parame

Q: Solve the DE using Variation of Parameters: y"+y = sec' x %3D

A: Given  The differential equation using variation of parameters. y''+y=sec3x

Q: solve homogeneous equation by linear method Tanx(dy/dx) + y = sec x

A: SOLUTION-

Q: Use variation of parameters to find the particular solution to y"+y' – 20y = - 3400 sin(3t) Y(t) = |…

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Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Here we can use the following formula  If z=fx,y, thendz=fx dx+fy dyδzδy=fx δxδy+fy

Q: The Integrating factor of the equation (x²y³ + xy) dy dx 1 is

A: We have to find the integration factor of the equation x2y3+xydydx=1. We know that integrating…

Q: Solve the differential equation by variation of parameters. y" + 3y' + 2y = cos(e*) y(x) =

A: Given differential equation: y''+3y'+2y=cosex               ...(1) Write the homogenous equation…

Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

Q: Solve the differential eqution y'-y=7e^x

A:

Q: Find the general solution analytically: (dy/dx) = 4 - y

A: Given data: The given differential equation is (dy/dx)=4-y. The given differential equation can be…

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

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Q: -X y" + 2y² + y = €²² ln x e^

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Q: Find the solution of the differential equatlor dy 3xeY, y(0) = 0 dx %3D

A: Consider the equation

Q: solve using the method of integrating factors. dy dx ==+x, y(1) = 3 х ||

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Q: - ydx + (x ++xy )dy= 0

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Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

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Q: ydx = x(1+ xy4)dy

A: Given ydx=x(1+xy4)dy ⇒dxdy=xy+x2y4y⇒dxdy+x-1y=x2y3

Q: Find the terminal value, lim y (r), for the solution of differential equation dy + 3z'y - 6z". dr

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Q: Y"+4y'+4y=e-2x Lnx

A: Given differential equation is y''+4y'+4y=e-2xlnx. Now auxiliary equation is m2+4m+4=0⇒(m+2)2=0…

Q: y"+y = e" what is the nonhomogenous(particular) solution of the given differantial equation?

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Q: Find the general solution of the equation dy + (tan t) y = cost dt

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Q: Solve the given third-order differential equation by variation of parameters. y" + 64y' = sec(8x)…

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Q: Solve the differential equatic y' = (x + y + 2)², Chart Area y(0) = 2 by setting u = x + y + 2.

A: y'=x+y+22let u=x+y+2     u'=1+y'     y'=u'-1

Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: Solve for the general solution of the given non-exact DE. y(y + 2x – 2)dx – 2(x + y)dy = 0 - -

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Q: Find dy/dx at the given point without first solving for y. x2 — бу — 37 %3D0 at (1, -6) | dy dx

A: This question is based on derivative.

Q: Find the integrating factor for the equation dy + sin(3x)y 223 dr

A: find the integrating factor

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.