3b) Find the green function correspondin. to the equation. dx² with boundary Conditions ulo) =0 and O= (1),

Q: xj dy - kry)

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Q: Using an appropriate substitution, solve the differential equation zdy/dz + y = 1/y²

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Q: Find afunction yp that is a solutionto the differential equation,y′′+y′=2e2x+cos(x).

A: To find the solution y"+y'=2e2x+cosx

Q: determine the general solution to thegiven differential equation. Derive your trial solution…

A:

Q: determine the general solution of the given differential equation that is valid in any interval not…

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Q: (3ху2 — у?)dx + (2х?у - 2у)dy - 0

A:

Q: Find the Wronskian of two solutions of the differential equation ty" -t(t-3)y' + (t5)y=0 without…

A: Given differential equation is t2y'' - t(t-3)y' + (t-5)y = 0

Q: 2. (D? — 2D + 5) у — 252? + 12

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Q: dy de + 2xy = 2xe-x².

A:

Q: Find the Wronskian of two solutions of the differential equation t²y" - t(t-3)y' + (t− 2)y =0…

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Q: Find the Wronskian of two solutions of the differential equation t²y" - t(t− 3)y' + (t− 2)y=0…

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Q: (e* + y)dx + ( 2+ x+ ye' )dy =0

A:

Q: 9. Find the particular integral of differential equation (D² +a² ]y =bcosax.

A: Particular integral of the second order differential equation.

Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =…

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Q: 2yy"=1+y'².

A: We have given differential equation ,  2yy'' = 1 + y'2 Here , substitute y' = u ⇒ y'' = u u'  Thus…

Q: sinh(3x) +1 y = 3 6 sinh(3x) – 1 y = 6 2 sinh(3x) – 1 y = O y = sinh(3x) O y = sinh(3x)+1

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Q: ll. SOLVE THE FOLLOWING BERNOULLI'S DIFFERENTIAL EQUATIONS. (SHOW YOUR COMPLETE SOLUTION) dy 2 4.…

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Q: owing dirferen tial equations: = xy dy %3D dy

A: Given that  The differential equation  2xdy/dx+2y=xydy/dx  To find the general solution

Q: 2ydx + x(2 + x²y) dy = 0

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Q: the semi-axes of the ellipse 4x^2 + 9y^2 = 36 are each increased by 0.15 cm, find the approximate…

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Q: 3. (D³ – 3D² +4)y = 40cos2x + 6

A: Given, D3-3D2+4y=40 cos2x+6 Its auxiliary equation is, m3-3m2+4=0⇒m+1m-22⇒m=-1,2,2 Hence,…

Q: (b) 1 When y = 1, dy/dt = but the graph does not have a horizontal v tangent line.

A: (b) dydt=et(y-1)2

Q: (3 şiny-5x) dx + 2x²cotydy = 0 hint: let 2 =sinu

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Q: Calculate the solution to the differential equation -ry 0 with bound- dr dy %3D ary values y = 1 and…

A: We have to find the solution

Q: Solve the Nou-linear differential equation casy Sinylla@şiny given that 4(0)=6

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Q: (D – 3D + 2) y = (1+ e-")?

A: I am attaching image so that you understand each and every step.

Q: What is the auxiliary equation associated with the second order linear differential equationd^2x…

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Q: dy Show that y 1 - + 2 is a solution of differential equation dx 1 -

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Q: THE

A: Please refer to the image below

Q: Please reply as soon as posible. Consider the function: y = C1e2x + C2xe2x + C3e-5x Find a linear…

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Q: The degree and order of the differential equation 1+ is = dy dz о 12, 1 O 1, 15 O 15, 1 O 3, 1

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Q: determine the general solution to thegiven differential equation. Derive your trial solution…

A: Given: y''+4y'+4y=5xe-2x

Q: By using variation of parameters, what is a possible value for u'1 for the differential equation y''…

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Q: Suppose that x = 0 is a regular singular point of the differential equation x²y" – x(x + 3)y' + (x +…

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Q: Given, (+) dz + (41) dy =i0 an exact differential equation. Az+1 Determine the value of A.

A: This question is related to exact differential equations, we will solve it using the condition for…

Q: Find the general solution of the given second-order differential equation. y" -y- 12y = 0 y(x) =…

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Q: Solve for the general solition of the followimg differential equation using FOLDE 2. (y - x + xy…

A: Given DE is  (y - x + xy cotx)dx + dy = 0.......(1) We solve this DE.

Q: d*y Obtain a particular solution for dx+ d²y + + dx² * + y = x³ + 2x + 1 dx

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Q: Find the Wronskian of two solutions of the differential equation ty" – t(t – 6)y + (t – 5)y = 0…

A: Directly use the formula for the Wronskian of a differential equation.

Q: Solve for first odrer differential equation    (x^2+cosy)dy+(3x^2+2xy)dx=0 where; x=0 , y=π/2

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Q: 4te dt TOT

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Q: The roots of an auxiliary equation are m1=4, m2=m3=-5. What is the corresponding differential…

A: If the root of the auxiliary equation is m1=α and m2=β, then the corresponding differential equation…

Q: Find the differential equations having as solution of y = x sin(xtc) .

A: We find the differential equations having as solution of y = x sin(xtc) .

Q: 3. (sin20 – 2pcos0)d0 = 2dp

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Q: Find the Wronskian of two solutions of the differential equation t²y" - t(t− 2)y' + (t−6)y = 0…

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Q: . Maiko is done computing for a GS of a Differential Equation. After applying the initial condition…

A: The particular solution of a differential equation is a solution which is free from arbitrary…

Q: What is the particular solution to the dy dx 4y differential equation 4 = with the initial condition…

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Q: Solve for the general solition of the followimg differential equation using FOLDE or FOBDE. 3. dy/dx…

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Q: Show that the differential equations are not exact. Determine the integrating factor to make each DE…

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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.