HW-1- 2dn Course Using the method of separation of variables, find the solution of the following equation a u ди 2. = u, given that u (x, 0) = 3 e-5x + 2 e-3x %3D ax ду

Q: Find the intersection point of the line 3x – 2y = 0 and the line passing through (-1, 0) and…

A: equation of one line 3x-2y=0 And second line passing through (-1,0) and is vertical (perpendicular)…

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 n = 4 (-x¹ + 22x³ -…

A: (a)How large should n be to guarantee that the Trapezoidal Rule approximation  to is accurate to…

Q: Step 2: Substitute whatever the variable equals into the opposite equation; use () 2x 12 y = 3x+2 2х…

A: Given: y= 3x+2 2x+y=12 To find: Substitute for the variable y in the opposite equation

Q: Solve for (x, y, z): 2x-2y+z=10 x+y-4z = - 17 3x-y + 2z = 13 O (4, -2, 1) O (1, -2, 4) O (2, 4, -1)

A: We have,  2x-2y+z=10 , x + y - 4z = -17 , 3x - y +2z = 13

Q: elimination of first degree variable:   2x-3y=2 4x-6y=11

A: The given system of equations consists of two parallel lines and two parallel lines never intersect…

Q: If the percent decrease is 25%, what is the common ratio?

A: Common Ratio The common ratio is defined as the amount between each number in a geometric sequence.…

Q: Find the point of intersection of the equations: x + y =1 and x2 + y2 = 5 Select the correct…

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Q: Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x…

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Q: Find the solution. (4D4 - 4D3 - 3D2 - 2D + 1)y = 0. A y = (c,+c,)e*+ (c,+cx)e/½ y= (c,+c)e/2+…

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Q: Solve using substitution y=2x+4 2x-y=-6

A: Given data: The expression for the first equation is y=2x+4. The expression for the second equation…

Q: The equation of OP is (x- 3)+ (y- 1)²=9. Without graphing, explain how you can determine whethen che…

A: Given equation of circle is, x-32+y-12=9

Q: (b) If you walk northwest, will you start to ascend or descend? O ascend O descend At what rate?…

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Q: y - y = x C. d. у +у — 7у — у + бу %3D 0 (4) y

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Q: Find the stationary point of each of the following equations and analysis the stability of each…

A: The given non-linear system is:…

Q: Find the solution. (D2+2D-3)y = 0 A y = B y = c,e- +cge²2 D

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Q: Using the method of separation of variables, find the solution of the following equation: = u, given…

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Q: (ху+ усotx)dy — у(хdу+ ydx) 30

A: Given the differential equation             (xy+ycotx)dy-y(xdy+ydx)=0

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: B. ty" – (t+ 1)y +y = t?

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Q: At what point does the graph of 3x+y=0 and x-y=D4 intersect?

A: Given: 3x+y = 0 y = -3x And x-y = 4 y = x-4

Q: Eliminate the arbitrary constant. y=Ax³+Bx³ (A B 7xy" - x²y + 15y = 0 D x²y '- 7xy" + 15y = 0 Cx²y"…

A: To find- Eliminate the arbitrary constant. y = Ax5 + Bx3

Q: Q2/ Classify the following equation as linear or not, and if not, what type of linearity it is: –…

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Q: (Зх — Зу+ 4)dx + (x — у)dy %3D 0

A: Given equation is (3x-3y+4)dx+(x-y)dy=0 This can be rewritten as, dydx=-(x-y)(3(x-y)+4) Take…

Q: The coordinates of a point on the line x+ y+1 = 0 which is at a distance /2 units from the line 3x +…

A: Given: The line x+y+1=0 which is at a distance 2 units from the line 3x+4y-2=0 To find: Coordinates…

Q: -ប៉ា + w Oy F= 2(x-G)y Oy + F = 2(x + G) Oy-G=-=-1(x-F) 2 Oy - G=-1¹(x+F) 3 2 T 0 -1- --2+ -3 5 2 3…

A: Given that Leo drew a line that is perpendicular to the line shown on the grid and passes through…

Q: Using the method of separation of variables, find the solution of the following equation: -2 = u,…

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