Given ey = x + y. Show that x +y (x + y – 1)3 d?y dx?

Q: If y =Aem + Be nx d'y -(m+n) dx? dy + mny = 0 dx Show that

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Q: Given that y =5u'+4u and x 1 hence find dy dx

A: Differentiation problem

Q: dy If e"y – y? = e – 4, then at x = and y = 2, 2 " dx - ||

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Q: Given f(x, y) (8a®y + 3xyf). Compute: dx?

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Q: A particular solution of 4x' d´y dx? +8.x- dy 4 is +y de

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Q: M(x,y) dx + (x,y) dy=0 to be exact

A: Solution :

Q: The value of 'n' to approximate [x dx by taking h = 0.1 using Trapezoidal Rule is О а.2 O b. 5 О с.…

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Q: when step Qal Evaluate the x²+2Xy + y? dy dx Size of x=0,2 and step size of y= 0.5

A: We have to solve ∫01∫02(x2+2xy+y2)dydx Given step size of x = 0.2 and step size of y = 0.5

Q: given y = ƒ(u) and u = g(x), find dy/dx =dy/dx = ƒ'(g(x))g'(x). y = -sec u, u = 1/x+ 7x

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Q: Let w = 4e" dx /A dy + aeª dx ^ dz and n = 7e*Y dx + 8e² dy + eY dz, where a E R. Find the value of…

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Q: Given y = x'e 2 2z - is: dy is: dz Solost ...

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Q: Given z = 3 In(t) and y = 9t then find dy dx dy dx2 |3|

A: givenx=3lnt,y=9t2

Q: given y = ƒ(u) and u = g(x), find dy/dx =dy/dx = ƒ'(g(x))g'(x). y = sin u, u = 3x + 1

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Q: Given y = ecos" a, at x = a dy > dx

A: Given that  y=e^(cos^3x)  To find the dy/dx at x=π/2

Q: For x> 0, 음 S"규E dt = Itt? %3D

A: For x>0, we need to find ddx∫1x11+t2dt. Leibniz's rule for differentiation under the integral…

Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: 3 Given 2 Lo L x²y dx dy, which of the following expressions is false?

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Q: Evaluate the following 1, $(3x – y)dx + (x + 5y)dy ,where C = x² + y? = 1 2.6(2y + 1+x5)dx + (5x –…

A: We have to evaluate the line  integral over the closed curve . Here I am solving first question if…

Q: Answer the given DE below: x (dy/dx) +y=y^2

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Q: Given that y = 7 ln u and u = 6x? dy Use the formula dx dy in terms of x. dx dy du to find dz du

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Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: ? the O.D.E's below is exact (x³ + y³)dx – (3xy²)dy = 0

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Q: 13. Differentiate y = e** with respect to x . ,3x+1 C (3x+1)e³x! D 3xe*+1 O A В D A

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Q: Which of the following equation is an exact D.E.? a) (x² + 1)dx –- xydy = 0 b) xdy+ (3x – 2y)dx = 0…

A: Let us consider the given equation M(x,y)dx+N(x,y)dy=0 The equation is exact if ∂M∂y=∂N∂x otherwise…

Q: B. Consider the following implicit expressions case find dy/dx in terms of x, y. 1. X2— у2 %3D 4 2.…

A: Given exppressions are 1.   x2-y2=42.  y+x2y2=x3. y2+x=y3

Q: Find a solution to the SDE dX; = X,(ydX; + tdt), where y ER is a constant and Xo = 1.

A: The given equation is dXt=XtγdXt+tdt. The given initial condition is X0=1. The integration formula…

Q: 5. Given y = af(+ 1), Find when x=1 if f(2) = 4 and f'(2) = 5. dx

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Q: Solve the first order o.d.e dy/dx=(1+y^2)e^x

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Q: The value of fox² dx could be approximated by using Trapezoidal Rule with n = 3. Find the values of…

A: The value of the integration

Q: given y = ƒ(u) and u = g(x), find dy/dx =dy/dx = ƒ'(g(x))g'(x). y = 6u - 9, u = (1/2)x4

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Q: Given r = 15 In(t) and y= 225 t then find dy dx d'y da?

A: Given that x=15lnty=225t2

Q: Given y=ae" +Be where a and B are constants. Show that d'y Ay. dx

A: Given that: y=αe2x+βe-2x…

Q: if y=u, u=v -1/2 and v=lnx, what is the value of dy/dx at x=e

A: Calculate the value of dy/dx and then put x=e .

Q: Given f(x,y) = ex cos y, Evaluate fy(2,0) O e² cos 2

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Q: Evaluate by Exact D.E. (2xy – 3x²) dx + (x² + y)dy = ( Oc= =y+x² + % 2 Oc = x²y – x³ + y? %3D 2 Oc =…

A: Given diff. eqn. is  2xy-3x2dx+x2+ydy=0

Q: Given dy = yx + e*y, y(0) = 1, h = 0.5 dx By using Euler's method, the value of y(0.5) is most…

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Q: d’y If y= cos 2x, then at dx? x = 0

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Q: given y = ƒ(u) and u = g(x), find dy/dx =dy/dx = ƒ'(g(x))g'(x). y = sin u, u = x - cos x

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Q: B. (y + e*seny)dx + (x + e*cosy)dy = 0

A: First we will classify the differential equation then find the general solution using the method…

Q: Using dy = 3 dx and dx = 0.03, what is dy when x = 2? 2V3X – 2 dy (Write as an exact decimal.) %D

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Q: Why is e^x selected as u and not e^2x (to get du /2 = e^x dx in the problem attached?

A: Consider the integral  ∫e2xe2x+3ex+2dx

Q: 56. Given that x+y - xy and that y dx dy when x 1 show that xy = e*

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 10. Given that y = at x = 1. e* X + 1 Find, in terms of e, the values of . 최 and dx dx²

A: (10). Given: y=exx+1   As we know that; The Power law; ddxxn=nxn-1 The Quotient rule;…

Q: Evaluate the following 1, 6(3x - y)dx + (x +5y)dy where C = x2 +y? 1 2.6(2y + 1+x5)dx + (5x- e")dy…

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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.