dt2 d²y e. ++ 4y = 8t – 10, y(0) = 1, y'(0) = 7 %3D %3D %3D

Q: dx 8х — 9у dt dy = x + 2y x(0) = 2 y(0) = 1 - dt

A: The solution is given as

Q: dx + dx dy e; dy = x +y Use elimination to solve: dt dt dt dt

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Q: dy dx ; x = 0, y = 1 , t= 0 dt dt 2) x = t2 + t y = t2 -t -00 <t < 00 %3D fall

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Q: 1 dx = 9 inches per second :- dt y = 1 + x2 (a) x = -3 dy in/sec %3D dt (b) x = 0 dy in/sec %3D dt…

A: Topic-derrivative

Q: + (4xy – 3x²) dy = 0, find an integrating factor of the form d equation. %3D

A: First we have to find integrating factor for given differential equation and with the help of…

Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

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Q: dx dy -- x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: We will find out the required solution

Q: dx – x = 4y, UTM dt dy + x = y + 3e', dt

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Q: at (x, y) = (1, 2) and z? = x2 + y² if dt dx = 4 and dt dy = 3. dt dz %3D %3D Find dz dt II

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Q: dy = 3. dt dz at (x, y) = (3, 1) and z² = x² + y² if dx = 1 and dt Find dz Preview dt

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Q: d y dy 14. dt2 +2, + y= 2 cos 2t dt У (0) —D у (0) — 0

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Q: dy The solution of (1 + y?) + (t – elan-ty Y = 0 is: %3D dt Select one: a. 1 t = etan-ly e2tan-ly O…

A: We have to choose the correct answer from the given condition according to the given condition

Q: Determine an integrating factor for the D.E. y3 x2 (v++)dx +* + xy*)dy = 0 1 3 4

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Q: Solve the following initial value problems using Laplace Transforms:

A: a.) The given initial value problem is,

Q: dx dy + y = x , dt = 3y dt dx dy 1.

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Q: Find the differential dy. (a) y = xV7-x dy (b) y = (1+x) dy

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Q: The integrating factor of the non-exact DE: y²dx + (xy – 1)dy = 0

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Q: [e?v ycos (xy)] dx + [2rev - xcos (xy) + 2y dy = 0 -

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Q: Find the differential dy. (а) у — ху5 xv5 – x dy = (b) y = (1+x)-9 dy

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Q: d'y dy dt Find the solution to the IVP + 9- + 18y = 0 where y(0) = - 7, (0) = 33. dt2 y(t) : Preview

A: Given that  The differential equation is  To find the solution of differential solution at given…

Q: Find the integrating factor a. (xy+y2)dx+(x2+3xy)dy=0   b. (y2e2x+1)dx+(2ye2x-ex)dy=0

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Q: dx dy - x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

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Q: Find an integrating factor for the DE y(4x – 3y – 3) dx +x(x- 2y – 1) dy=0_

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Q: Find the differential dy. (a) y = xV10 - x dy = -2 (b) y = (1+x) ? dy =

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Q: dx dy - x – 2y = 16te', 2x - dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: The given differential equations are                                  dxdt-x-2y=16tet ..............…

Q: b- dy +2y=0; y=1 at t=0, y(0)=1 dt

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Q: 6. dy dx + y?x = sin y, dx ay = 7. dt dt 8. Σa (x) dx) d0y = f(x), where d°y = y, dx°

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Q: The solution of dy/dx = y2 with initial value y (0) = 1 bounded in the interval %3D

A: Introduction :

Q: d'y dt2 dy + 4 + 3y = 20 sin(t) where y(0): -2, (0): - 4. Find the solution to the IVP %3D

A: firstly we find out CF and then PI and  general solution is  y(t)=CF+PI

Q: d²y z + y = e-2tsin(t) , y(0) = 0 and y (0) = 0 dt2

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Q: dy (c) -y = e* sin(2x) Integrating Factor Marks] y = 1 when x = 0

A: This question is based on solution of linear differential equation.

Q: (y')² – 3yy' + xy = 0 12 +y = x \dx², S + (S + = 0 dt² dt² dy x*y" + xy" = ex ds t2 \dt², () - t=1 –…

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Q: (а) dy/dat = sin 2x. (b) dx + e dy = 0. (с) zdy/dx — у. (d) cosec y dx + sec2 x dy = 0. dP (e) dt Р-…

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Q: Solve the homogeneous DE ( xy) dx - (x + 2y)^2 dy = 0

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Q: D. Identify the linearity of the following equations. y°dx + xdy = sin y dy 16. dzy +x- dt2 d?x 17.…

A: Given that:                                 NOTE: As per our answering guidelines, we can only…

Q: dy + 2.xy= 5x² is dx The integrating factor of

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Q: dy + 2 dy + y = sinh 3t – 5 cosh 3t ; y (0) = -2, y (0) = 5 II %3D |3D | dt? dt

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Q: 2 In(t) and y=4 t2 then find %3D %3D dy dx d'y dx2

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Q: dx = -y+y(x² + y² dt dy = x – x(x² + y²) - dt

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Q: What is the solution of given initial value problem? d²x = y + sin t dt2 d²y dx + cost dt dt2 æ(0) =…

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Q: 3. Linear DE of Order one 2y(y? – x)dy = dx 4. Bernoulli's Equation 3dy – 4xy dx = 3x²y*e-2x² dx

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Q: dx T2 +2 and dt dy 2. Find at I = 2 if y = dt dy dt

A: Solve for dy/dt at x=2

Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

A: We have to check whether the given differential equations are linear and homogeneous or not. A…

Q: dy dæ at x = 2 if y = 3x + 5 and dt Find - 2. %3D %3D - dt dy %3D dt

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Q: d²y dx² -3 dy dt 4y = 3 sin x given y(0) ) = 0 and y'(0) = 0

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Q: ii- (x* + y) dx - ry dy = 0, y(2) = 1 (using Integrating Factors)

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Q: Find the integrating factor. a. (xy + y2)dx + (x + 2y- 1)dy = 0

A: We have to solve the problem

Q: dy x2 + y2 if dx Find at (x, y) = (5, 6) and z? dz dt = 9 and = 7. dt dt dz dt Additional Materials

A: To determine the derivative.

Q: Find the general solution to the following equations. dx dy 1. + y = x , = 3y dt dt

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Q: Find an integrating factor for the linear DE of order one dx + (2xy – 1)dy = 0. (1)y? (2) ey² (3) x²…

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