Use the method of separation of variables to solve yu, + xu, = xyu , U(x,0) = 3e*

Q: 4 t2 – 4 dt -1

A: We have to find the integral using piecewise method.

Q: Solve using crama's rule: 2x - 2y + 3z = 13 5x - y + 4z = 11 x + 3y - z = -10

A: We solve the system using Cramer rules

Q: Find the general solution of y' = y secx

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Q: Obtain the general solution valid near the origin: х(х-2)y1+2(х-1)у - 2у %3D0

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Q: Solve: xy + y + 4x³y¹ = 0 O 6ry³ + Cr³y³ = 1 O 15r y³ +Cr³y³ = 4 O9r³y³ + Cr³y³ = 5 O 2r³y³ + Cr³y³…

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy + y?

A: Idea: after separating x,dx and y, dy terms together. we take integration on both sides . after…

Q: dz and dy dz 3. If x? – 3yz2 + xyz – 2 = 0, find -

A: In this question we have to find the dzdx and dzdy.

Q: f(x) = 2+ 3x² – 8x3 -

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Q: dy りー! り(-)ニ。 x+3 2, xy' =1+X ら(4)=0

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Q: Obtain the general solution valid near the origin: x(x − 2)y" + 2(x − 1)y' − 2y = 0

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Q: Obtain the general solution using variation of parameters y''+y = (csc³x) (cotx)

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Q: Solve through finite differences with four subintervals: + y = 0, y'(0) + X(0) = 2, dr² x ( + 7) + (…

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Q: Solve 2 secx- 5 secx+ 2 = 0 on the interval x e [0, 2x] %3D

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Q: (x) + Find the general solution аху- х+у о у-xlncxЈtc 2 x² Ў= х²-хутуг у-х- х Нихте з y = x + y + y…

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Q: I have equation 3x(y-x)=0. Is it true that x here is equal to 0 and y is equal to x? How can I show…

A: To check:  Whether x here is equal to 0 and y is equal to x. Given information: The equation is…

Q: ELIMINATE THE ARBITRARY CONSTANTS y = x² + ax + be¯*

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Q: use Separation of Variables to find the general solution. yy' = x

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Q: Solve using separation of variables:   y'-xy+y=2y

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Q: Use method of variation of parameters. y" +2y-8y = 2e-2x - e-x.

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Q: 2 xy' + 3y = 3 –

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Q: 2. Solve by using an integrating factor. (a) y' + 2ty = 2te¯ %3D

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Q: ln (x−4) + ln (x+1) = ln (x −8

A: We can use properties of log to slove the given problem. If we have  ln x + ln y Then we can write…

Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: Solve using D-Operator 3. y + 2y + y = x²

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Q: Solve 1) y" + y' – 6y = x2 2) y" + y' – 6 = tx Where t: constant

A: (1).   The given differential equation is:  y''+y'-6y=x2 The characteristic equation of the…

Q: Use Variation of Parameters to obtain the General Solution 1. y +4y 4-sx2x

A: Solve the given problem.

Q: Differentiate: y = 4cos (-)

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Q: Q.4 Use the method of separation of variables to solve : xyu̟ +2u, =0, U(x,0) = 3x* . %3D

A: Standard partial differential is given as: p∂u∂x+q∂u∂y=r Lagrange method for finding solution for…

Q: Solve for x, y z from X - 1 1 2 Z 3. 6 6

A: 2x-113y=2z66

Q: 7. Solve: dy x + 3y dr 3x + y

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Q: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

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Q: Define properties of Solutions of y' = y?

A: Solution: Consider the given equation is y' = y First, find the solution to this equation. dydx  =…

Q: use Separation of Variables to find the general solution. y' = x sec y

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Q: y" + 2y" + y" = x + eX %3D

A: Given the differential equation y'''' + 2y''' + y'' = x + ex We find the particular solution form…

Q: Solve for x,y,z if x+ 2y + 2z=0 2x + y + 2z = 0 2x + 2y + z = 0

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Q: 5. Use variation of parameters method to solve а. a. y" – 2y' + y = 1+x2

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Q: y= cot(-2x) y4 3 12T 37 -1- -2+ -3+

A: We have to find

Q: (1 - V2) dt 44. 46. (2z – 3) dz - 3

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Q: what is the solution of equation 2ydx + (2xlogx - xy)dy = 0

A: Given differential equation is. 2ydx+2xlogx-xydy=0

Q: List the roots of the auxiliary equation for a homogeneous linear equation with real  constant…

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy 2 2 + y?

A: using seperation of variables  and then integrate....

Q: Obtain the solution using Integrating Factors Found by Inspection 2x 5y ′ = y(3x4+y2)

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Q: Solve for y when x=o degrees: y=2sinx

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Q: Solve (x² - 4xy-2y²) dx + (y² - 4xy - 2x²)dy = 0 By using the method of the exact equations 1-…

A: The given problem is to solve the given differential equation by using the method of the exact…

Q: 7. Solve: ydx = 2(x + y)dy

A: Answer

Q: Sa 3dx 1. (x+6)Vx+4 2. V-1+2 dt

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Q: Solve using variation of parameters: y" – 2y' + y = -

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Q: ng through the point that is ion. 10. (-3, -2); y = x – 2 12. (-1, -6); r + 3y = 6

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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.