Write the equation for the curve that has slope of 2y/x for each point P(x,y) on it and passes through the (3,4) point.

Q: Find the equation of the tangent line to the curve x' + y' = 6xy at (3,3). Write the equation in…

A: Given the curve x3+y3=6xy We need to find equation of the tangent line to the given curve at (3,3)…

Q: Find the equation for the curve in the xy-plane that passes through the point (1, -1) if its slope…

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Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of at any point…

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Q: At what point on the curve x = 3t2 + 5, y = t3 - 5 does the tangent line have slope ? (х, у) %3

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Q: Find an equation of the curve that passes through the point (1, 3), and has the given slope y′ =…

A:

Q: At what point on the curve x 3t2 + 1, y = t3 - 5 does the tangent line have slope ? (х, у) -

A: We have given curve as x=3t2+1         ⋯⋯1y=t3-5           ⋯⋯2 From the equation (1) and (2), on…

Q: Find an equation for the line perpendicular to the tangent to the curve y = x°- 16x + 6 at the point…

A: Given: y=x3-16x+6, 4,6 we know that equation of line which perpendicular to tangent at given point…

Q: find the slope of the curve at the point indicated.

A: We need to find the slope of the curve at the point indicated, y=5x-3x2,x=1

Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

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Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of y/x2 at any…

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Q: At what point(s) on the curve x = (x, y) = 6t² + 4, y = t³ - 7 does the tangent line have slope?

A: This question is related to parametric curves and slope of tangent, we will solve it using given…

Q: Find the slope of the tangent line to the curve – 2a2 + xy + 4y³ = - 6 3 at the point (- 2, 1).

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Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: Find the slope of the curve x2 + y3 = 2 at each point wherey = 1

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Q: Find an equation of the curve that passes through the point (3, 1), and has the given slope y′ = −…

A: Given that y'=-y5xdydx=-y5x

Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ?

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Q: Write the equation of the tangent line to the curve (a lemniscate) 2(x2 + y²)“ = 25(x² – y²) at the…

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Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

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Q: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

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Q: ) Find the equation of the line normal to the curve x'y+ y'x = 10 at point (1,2).

A: Slope of a normal to the function y=f(x) at point m,n is given by the value of -dxdy at m,n Equation…

Q: Find the equation of the tangent line to the curve y=1-x² that is parallel to the line 2x-4y=8

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Q: Find the slope of the line tan gent to the curve of 2y³ + xy + 1 = 0 at the point (-3, 1) .

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Q: Find the slope of a line tangent to the curve of the given equation at the given point. y = x2 - 3;…

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Q: Find the equation of the family of curve whose slope at any point (x,y) is (x+1)/(y-1)

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Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: Find the equation of the curve that passes through the point (0, 2) and has a slope of at any point…

A:

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: The slope of the curve when x=e is y = (In 2x)?

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Q: find the slope of the curve at the given points (x2 + y2)2 = (x - y)2 at (1, 0) and (1, -1)

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Q: Find an equation of the curve that passes through the point (0, 2), and has the given slope y′ =…

A: y'=x4y, (0,2) Formula ∫xndx=xn+1n+1+C

Q: Find the equation for the line tangent to the curve 2exy = x + y

A:

Q: Find the equation of the curve that passes through the point (8, 6) if its slope is given by dy =6z-…

A: We have to find y

Q: Find the eqaution of the curve that passes through (0,1) if its slope is given by y'=1/2X at any…

A:

Q: Find an equation of the curve that passes through the point (1, 1), and has the given slope y′ = −…

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

A:

Q: Find an equation of the curve that passes through the point (0, 6) and whOse slope at (X, y) is X/y.

A: Given that: Slope of the curve at (x, y)=xy

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

A:

Q: Find the equation of the tangent line to the curve y = x2 – 5 if the tangent line is parallel to the…

A: y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.

Q: At what point on the curve x = 9t2 + 3, y = t3 – 2 does the tangent line have slope ? (x, y) =

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Q: Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y.

A:

Q: Find the slope of the curve at the given point. y3= x3/2a-x   at (a,a)

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Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

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Q: ) Find an equation of the line tangent to the curve y = x²e²-3 at a = 3.

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Q: At what point on the curve x = 3t2 + 4, y = t³ – 6 does the tangent line have slope ? (x, y) = ( 3,…

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Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: Find the equation of the family of curve whose slope at any point (x,y) is 3x^2+4

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Q: At what point on the curve x = 6t2 + 2, y = t3 - 5 does the tangent line have slope (x, y) =

A:

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,

Q: At what point on the curve x = 3t2 + 1, y = t3 – 5 does the tangent line have slope ? 2

A:

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.