findthe solutionof the differenta eqration- dy 2X+y-) X 4X+2Y+5

Q: Find the number of non negative solutions to x+y+z= 21. With the conditions that x < 3, y ≥ 2, z ≥…

A: Given that x+y+z=21 with the conditions x&lt;3, y≥2, z≥4

Q: Solve y′′ + 4y = u2(t), y(0)=1, y’(0)=2

A:

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

A:

Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: Determine the interval in which solutions are sure to exist. !!! y (4) + 3y + 2y = t Valid on the…

A:

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: Show that y = ex + 3xex  is a solution of y"-2y'+y=0

A: The given differential equation is,

Q: Solve the dff oq 2. 3. 3. %3D 1

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

A:

Q: 5-4y2 dy 3+2y

A: To evaluate ∫5-4y23+2ydy

Q: x(1-х)у" - Зу' + 2у %3D0

A:

Q: 3. zy if y + x² – 3xz = 222

A:

Q: Determine the interval in which solutions are sure to exist y(4) + 4y" + 2y = t Valid on the…

A: image is attached

Q: What is the general solution of 3 (3z + y') dz – 2zydy = 0?

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Q: What is the solution (ry – r) dr + (x²y + y) dy = 0 when 2 and y = 1

A:

Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: Verify that y, = e2x and y2 = e5×are solutions of у" - 7у' + 10у %3D 0

A: We have to verify that the functions y1=e2x and y2=e5x are solutions to the given differential…

Q: Obtain 2 linearly independent solutions valid near the origin for x>0 2хy" + 5(1 — 2х)у' — 5у %3D 0.…

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Q: A) (:: :) Verify that y = c₁cos(3x) + c₂sin(3x) is a solution of y' +9y = 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: If y+3y = 8 then g- solution is %3D a- y + 6 = 1 b- In (8 -3y ) = x + c %3D

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Q: max z = 2x + 8y %3D s.t 3x + 9y 12 х, у > 0

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Q: Obtain the family of solutions 1) xydx – (x² +3y² ) dy = 0 2

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Q: 4. Solve eu, - uu, = 0, u(0, y) = -y %3D for small |r.

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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

A:

Q: Determine the interval in which solutions are sure to exist. y(4) + 5y" + 3y = t Valid on the…

A: Given differential equation is y4+5y''+3y=t. We have to determine the interval in which solution are…

Q: dz Find at (2, -2, 1) if x² + y? + z2 6xz + 6yz + 21

A: Given equation is x2+y2+z2=6xz+6yz+21 We have to find ∂z∂y at 2,-2,1

Q: If y = (x+1)/(2x - root x' then y' will be?

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

A: 2x-113y=2z66

Q: The solution interval of 2y +1≥3 or 3y1 or y< -11 BO

A:

Q: 3)으 rcose de Jsine 1-x2 d ¿= xp 2

A: LEIBNIZ RULE

Q: VAy 5-y-z 15z dz dz dy 2y2 2-y-

A: SOLUTION-

Q: 3/2 y 3. dydx 3 X

A: A detailed solution is given below

Q: 6- Show that y = xsinx is a solution to y +y 2cosx

A: The given differential equation is: y''+y=2 cos x

Q: 6) qyo -x² +2x + S%y +62=0 sty

A: 6)

Q: Show complete solution. 6y^2dx-x(2x^3+y)dy=0

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

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

Q: I have included one line of the whole solution in the questionnaire. Analyze if this included part…

A: y = ln(1-5y2 +y3) now differentiate it y' = (-10y+3y2 )/(1-5y2 +y3) here between (+) sign so there…

Q: (): Suppose y = cjex + czetx is the general solution to y = Ay. What is A %3D %3D ? We don't have…

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Q: Obtain the general solution valid near the origin: x(х — 2)у" + 2 (х — 1)у' — 2у 3D0

A: The differential equation has singularity at the origin. So we find the solution by Frobienius…

Q: 6- Show that y = xsinx is a solution to y= + y = 2cosx

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Q: Verify that y = ODE y" + 3y' + 2y = 4x². -4e-x-2e-2x + 2x² - 6x +7 is a solution of the SHOW ALL…

A: We have to verify that y=-4e-x-2e-2x+2x2-6x+7 is a solution of the ordinary differential equation…

Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0

Q: Eliminate the arbitrary conutantu 2. %3D y= ax + be

A:

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.