T:4x-34+2-2-0 Tz: dx+ Sy-32+4 = 0

Q: 6. If x(t) = e' +1 and y=2e²ª are the equations of the path of a particle moving in the xy-plane,…

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Q: Solve the equation (x - xy + y )dx - xydy = 0. %3D O (y - x) el:) O (y - x) = cel)

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Q: Q4/ solve the following equations. d²y dy + 81 = 0 dx2 dx

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Q: al equation - y² , y(1) = 2 is hod with step siz nd off to 2 place

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Q: find the general solution of the given equation. y'' + 16y = 0

A: Given , y''+16y=0Lrt , y=Aemx≠0be the trial solution of the given differential equation .Then…

Q: For x = t3 + 2, y = 3 – t, give an equation in terms of x and y.

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Q: The solution of (D² – 4D+13)y 0 5 2x (A eix . Be Jox (A ex + Be)

A: D2-4D+13y=0 The auxiliary equation is m2-4m+13=0 ⇒m=4±-42-4132⇒m=2±3i

Q: (D'-3D+4)y(x) = xcos(2x) equation

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Q: Find all values of r for which the function y = e^(rx) satisfies the equation y'' + 5y'-6y=0

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Q: 6. Find the equation of the motion. 12 and s=3, v=1, when t=2 t4 Given: a ==

A: Given: a=12t4  ……1   Also, At t=2:v=1……2At t=2:s=3……3

Q: Find an equation that repesents C(t) = -2i + 3eit, 0 ≤ t ≤ 2π but traveling in the opposite…

A: Equation travelling in opposite direction

Q: b) Now, start with the exact same equation as before, i.e. Vz+ Vj= 5,

A: Given  x^(1/2) + y^(1/2) =5

Q: Find the values of r for which y = e"* satisfies the equation y +2y -8y=0

A: The given differential equation is: y''+2y'-8y=0

Q: W3 y = dy solve for a-w' dw HIN

A: To find: Solve using chain rule for dy/dw

Q: Solve for h: rh 22. Then rewrite 2ar? + 2arh in terms %3D of r.

A: Given πr2h=22value of  h⇒h=22πr2

Q: SOlve the differentilal equation d²y d*y 4- d³y + 7. dx2 14 | dx+ dx3

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Q: B. Find the x and y of the following equations. 1. (x + jy)² = 5 + j3

A: Solution

Q: Solve the given DE. (D³ + D² + D+ 1) y = 0 ; y (0) = 2, y' (0) = 2, y" (0) = -4

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Q: Q1. Solve the following first order equations: (a) (r²y² + 1)dx + 2x²dy = 0, use the substitution ry…

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Q: x² + y)dx + xy dy = 0

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Q: у dx - ( х + х2 у) dy %30

A: Given differential equation is ydx−x+x2ydy=0.....1. First we have to reduce the given differential…

Q: The solution to the equation is ged (D²-D-6)y(x) = xe %3D 1 1 -xe" (5x-2) - y,(x) 50 1 د. غير ذلك…

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Q: Solve the following d'y 8- + 16y = 9e2 dx? d'y dx4 using the method of undetermined coefficients.

A: The solution is given as

Q: a²y³ + x(9+ y²)/ = 0 %3D llowing the steps below: a) Show that the equation is NOT exact.

A: Checking the exactness of given differential equation

Q: The foci of the below equation are x² – 4y² + 2x + 8y – 7 = 0

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Q: x+ y = 0 3x- 2y 10 ch of the following ordered pairs (x, y) ystem of equations above?

A: From the given data: x+y=0 3x-2y=10

Q: 3. Find all of the equation. (а) у —х (c) y' = x Inx (e) y" = 2xe*

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: ut the equation y 4x2 - 32x + 7 into the form y = (x – h)² + k: %3D nswer: y =

A: We need to make whole square .

Q: Q4|| A|| Find the value of (x) by solving the following equation: 2 1 4| -1 0 = 2 dy -2 41 -2 Jy2 –…

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Q: Find a solution of x dx = y²-y that passes through the indicated points. (a) (0, 1) y = (b) (0, 0) y…

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Q: Solve the following equation for c: 1 2-c-z 2-²-y 1 dz dy da 10

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Q: (2x2+y)dx + (x2y-x)dy = 0 solve the equation.

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Q: Use an appropriate substitution to solve the equation 9. y3 %3D 13 and find the solution that…

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Q: Q4/ solve the following equations. d²y dy + 81- = 0 dx² dx

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Q: Q4|| A|| Find the value of (x) by solving the following equation: 2 1 4| -1 0 = 41 dy |-2 -2 Jy2 – 4

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Q: d?y =6- 9x and which passes through the points (0, -1) dx2 Find the equation of the curve for which…

A: Differential equations

Q: d?y -=6-9x dx2 Find the equation of the curve for which and which passes through the points (0, -1)…

A: We will do this question by checking the conditions for the given options.

Q: dy - 5y = 2(x + c)?, Given that dx ceR Verify that the solution of the equation is as follows: 4 4 +…

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Q: Solve the he (D’+ 4D+4)y(x) = 5e equation y,)-(2x+1)e - y,) (2x+1)e y,(x) (2x-1)e 32

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Q: Q2/ solve the following equations. (x² + y²)dx + xydy = 0

A: Here, the given differential equation is: (x2+y2)dx+xydy=0...(1)

Q: Q1. Find a general solution of the following equation: 2x(dx + dy) + y(dy – 5dx) = 0

A: Here we have,  2x(dx+dy)+y(dy-5dx)=0

Q: B/Solve the following equation - 4t + 6y = t³ + 1 dt2 dt

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Q: Solue the differantial equation Dxy'+3y=6x3

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Q: A car is driving away from the base of a 30-meter-tall building. y 30 metres Car (a) Which of the…

A: We have given right angle triangle  Using Pythagoras theorem  (Hypotenuse)^2 = (Perpendicular)^2 +…

Q: D. y" – = 0 3y" + 3y' - y =

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

Q: Match the equations with the solutions. a. 9e3 = 27 X z 1.099 b. 9e* = 27 Xz 1.022 c. 9e3x -4 = 27…

A: a) Given 9e3x=27e3x=27/9e3x=3Taking ln on both sidesln e3x=ln(3)3x=1.098x=1.0983∴x≈0.366 b) Given…

Q: Y2 = Y1(x) / "dx (5) as instructed, to find a second solution y,(x). у" - 8y' + 1бу %3D 0%; Y1 = e…

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Q: Solve (D – D4 + 4D³ – 4D²) y = 32 cos (2x) – 20e¬× %3D

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Q: Q/ Solve the DEs: 1-a+yxdx+(1+x)dy = 0

A: 1-(1+y2)dx+(1+x2)dy=0