(a) [10pts| y' = (x2 – 4)(3y + 2), y >0 dy 3y+2 = dx (x-4) » yt=ce >y=ce -en lyt > en cyt=) = x²1zx+C. x-4x+ C 3

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e %3D 5. (x2 - 1) dy =…

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Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

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Q: dx dy at z = - 5 if y = 3x-3 and dt Find -1. dt dx dt

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Q: e particular solution of the differential uation x^2 dx - (y+1) dy 0 if y(0)=1 2y^2+3y-6x^3+6= 0…

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Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

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Q: Fromthe partial differential equation by elimaniting the arbitary function ø, and ø, from z= 0 (x…

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Q: dx =- 1. dt dy at x = 2 if y = 4x° – 2 and dt %3D Find - dy dt

A: Given: y=4x2-2 and dxdt=-1 To find: dydt, when x=2.

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

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Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

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Q: Solve the differential equatons x(2y + In ax) dy + (x+y)dx when x=3 y=Ź y= 2 1.

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Q: How does the Fundamental Theorem provide a solution to the initial value problem dy/dx = ƒ(x), y(x0)…

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Q: 2. Identify the 3rd order nonlinear DE. 3 (dy` A. ( +x³y – xy³ = 0 dx. d³y d²y +y dx2 В. = 0 dx3 d³y…

A: Check each options while it is 3rd order as well as nonlinear differential equation.

Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

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Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) .…

A: Given equation is

Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

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Q: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?

A: We have, a particle moves on the graph of a function given as y2=x+1 Differentiating both of the…

Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

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Q: 11. Find the length of the curve x = on the interval [2, 4] (integrate with respect to y) 12y3

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Q: dy Kutta method to integrate = 4e0.8x step size of h 0.5 and an initial condition of y = 2 at x =0…

A: 4th order Runge-Kutta method…

Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

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Q: 4 I. dx3, (d³y\ dy + 2- dx = sin x *+ O) + = In y. 3 II. dx dx dx d³y III. dx3 d²y , dy -2 + dx2 = x…

A: To identify which of the given differential equation is linear.

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: y (y^3-x) dx + x(y^3+x) dy=0_At· muon

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Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: Estimate Ay using differentials. 1/33x-1, y = x ¹/3 e³x-1. a = 1, dx = 0.1

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Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

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Q: dy Use 4th order Runge - Kutta method to integrate step size of h = 0.5 and an initial condition of…

A: Let dydx=f(x,y) and the initial condition is y0=f(x0) . The 4th order Runge-Kutta method uses the…

Q: OBTAIN A FAMILY OF SOLUTION 2. (x - yny + y In x ) dx + x CIn y - In x)dy =0 3. [x - yarctan…

A: This question is related to differential equation.

Q: 1. sinx siny dx + cosx cosy dy = 0 %3D 2. [2xy cos(x2) – 2xy + 1]dx + [sin(x²) – x²]dy = 0 3. y?dx +…

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Q: 4) (2x + y cos xy) dx t x cOs xy dy - o cOs xy) dx t X COS Xy dy COS

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Q: Find dy dt dy dt at x = 3 if y = 5x² + 3 and dx dt 2.

A: Given:-y=5x2+3dxdt=2 at x=3To find : dydt

Q: The transversality condition holds for the partial differential equation X4x +Uy=0 with the initial…

A: In the given question we have to check the transversality  condition of the given P.D.E s.t xux+uy=0…

Q: Find the integral surface passing through the curve 1 T: z = sin y + e' +- x = 0 8 of the partial…

A: In this question, we solve the partial differential equation by using the surface condition.

Q: y² cos x - 3x3y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e x² - 1) dy = ((1 + x)2 -…

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Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

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Q: (x – y ln y + y ln æ)dx + x(ln y– In x)dy = 0 - - %3D

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Q: Find dy dy dt at x = z - 1 if y = -5x² + 3 and dx dt 5.

A: topic:- derivatives

Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: 1 transforms the equation x dy + y = xy2sin(x) into The change of dependent variable y = dx dv A.…

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Q: Use Euler's method to numerically integrate dy -2x3 + 12x2 – 20x + 8.5 %3D dx from x = 0 to x = 0.5…

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Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

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Q: (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y =…

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Q: d²x + 16x = 1 + 2 sin 4t dt2 dx (0) = 0 x(0) = 0, %3D dt

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Q: THE IVP

A: Consider the provided differential equation with initial condition is,

Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…