Use GeoGebra to create a direction field for the differential equation dy/dx = x^2 − y. Then use GeoGebra to draw an approximate solution curve that passes through the indicated points. This will have 4 different curves on one picture. Submit your screenshot/graphics file. a) y(−6) = 0 b) y(0) = 1 c) y(0) = −4 d) y(8) = −4

Q: Solve the equation dy, 3y + dx +2 = 3x, y(1) = 1.

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Q: Find dy/dx of * ye2x + xe2y = 0. %3D

A: This is a derivative problem

Q: Let y = (x² + 5)5. Find the differential dy when x = 3 and dx = 0.5 Find the differential dy when x…

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Q: dy Find for each equation and simplify fully. dx (17x² + B) (11x – A)° (а). у- (5x+4)°

A: Given                             y=17x2+B511x-A85x+46; A=4, B=8 we have to find derivative of the…

Q: Let xy = 2y + x. If you implicitly differentiate this dy equation, and then solve for you dx (a-y)…

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Q: x(2y – 3)dx + (x2 + 1)dy = 0

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Q: dx ex -1

A: Let ex=t ⇒exdx=dt    dx=dtex          =dtt

Q: (0²+20+5)y= sinhx

A: D2+2D+5y = sinhxcan be written as:

Q: Let y = (x² + 5)5. Find the differential dy when x = 3 and dx = 0.5 - Find the differential dy when…

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Q: If y' = and y (In 3) = 3, find y.

A: Here the differential equation is y'=exy2, with initial condition y(ln(3))=3.

Q: Q2: find y' y= 33xelnx²

A: We have the given function : y=33xelnx2 We have to find the derivative of this function.

Q: Let y = V5- z. Find the differential dy whenz= 2 and dr = 0.1 %3D Find the differential dy whenz= 2…

A: y=5-x

Q: Find the slope of the graph of the equation at the given point. (If an answer is undefined, enter…

A: we have been given the slope of the equation xy=x-2y,at (4,1) it can be written as  xy=x-2y

Q: dy %3D xp

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Q: 8. (Зх — у — 1) dx + (9х — Зу + 4) dy %3D0

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Q: 22. y = sec 4(4+x³) 5

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Q: 30. y= sin x ex+5

A: Consider the given function. y=sinxex+5

Q: A tornado can be represented in polar cords by the velocity 7=4, +. Show thau streamline from…

A: Given that V→=-arir+briθ By comparing the given equation from the general equation V→=urir+uθiθ.…

Q: The pressure, volume and temperature of an ideal gas are related by the equation 8.31T P(T,V) = V…

A: Given, P(T,V)=(8.31T)/V At centre V=12litre and T=310k

Q: 5

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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.