b. (3xy3 + 4y)dx + (3x?y² + 2x)dy = 0; when x = 1, y = 1

Q: dy y² tion + dx x² है || Y 8

A:

Q: d/dx (dy/dx)` x=1, , where y = x3 + 2x - 11

A: To find: The value of ddxdydx at x=1. Given: The function is y=x3+2x-11. Formula used: Power rule of…

Q: d'y dr2 dy - 2 +y=3 e4x, given y(0) dx 1 and y'(0) =4; 3.

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Q: (x*y - 2xy) dy dx 2.

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Q: a. (2ry*e + 2xy + y) dx + (r²y*e -x²y² – 3x) dy = 0; when x = -1, y = 1

A: As per our guidelines we are supposed to answer 1st question only. Please repost rest questions...…

Q: -3 (x + y)dx dy

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Q: (b) y = u4 and u = 9x2 – x + 7 dy du 4u³ ,3 du 18x – 1 dx dy dx &x(9x² – x + 7)³ × II

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Q: find d^2y/dx^2 if y= 17/ x^3

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Q: If xy + y2 = 1, find the value of d2y/dx2 at the point (0, -1).

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Q: y (x² + y²) dx + x (3x? – 5y²) dy = 0l -

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Q: y-dx + (x2 + 3xy+ 4y²) dy = 0, when x = 2, y=1

A: Explanation of the answer is as follows

Q: SOLVE THE FIRST ORDER DE. (x³ + y*)dx + 8y³xdy = 0 when x = 4, y = 2

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Q: .3 9. dx dy y2

A: Find the double integration.

Q: Evaluate the integrals

A: The given integral is ∫02∫03y∫x2+3y28-x2-y2dzdxdy.

Q: (2x² – ye")dx – e dy = 0. - -

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Q: The equation dy - ydx = [-x*y^3* e^(-2x) ]dx is linear in x but not in y. True or false?

A: Given that dy-dx=-xy3e-2xdx.

Q: 36. dy dx y=x2/3

A: The given integral is ∫01∫x231xey4dy dx. From the above integral, the region is given by…

Q: (x'+3xy²)dx +(3x³y +y')dy = (

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Q: (y* - 2xy)dx + 3x?dy = 0; when x = 2, y = 1

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Q: dy dx 2xy + 6x + (x²-4)-

A: Solution of given question is written in below steps.

Q: If 3x2 +2xy +y² = 2, then the value of dy at x=1 is dx

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Q: (x² + y²)dy dx 7.

A: Given  ∫-22∫04-x2(x2+y2) dydx

Q: dy/dx = 3xy/(x^2-y^2)

A: Given a differential equation, dydx=3xyx2-y2. Clearly, the above equation is a homogeneous equation…

Q: calculate  d^2y/dx^2 for y=e^7-2x + 12

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Q: dx 2x dy y 3.

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Q: I Solve the fllowing FODF 2y(x+y+2) dx + (y²-x²_ 4x-1)dy = o when x=2,y= 3

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Q: dy 34. = ty² +3t²y with y(-1) = 2 %3D dt

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Q: d'y dx +8y = 2x – 5 + 8e **, y(0)=-5, y'(0)=3. y"(0)=-4

A: Given the differential equation            y'''+8y=2x-5+8e-2x with initial conditions y(0)=-5,…

Q: ( 3x³ - xy² 2 3xy+y dy 3 dx = 1 |

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Q: 2) dx dy x²+y² 2хy ||

A: Integrating the given equation.

Q: If y^3−3xy=18 then dy/dx

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Q: Find 2," dy d²y dx ' dx? d3y and from: dx3 3. x = 1 – t? and y = 2t3 – t2 + 1

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Q: find d^2y/dx^2 for y^2 + 2y=2x+1

A: Consider the function,

Q: and Y=-2 when X=Z dx

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Q: /16- y? (x² + y?) dx dy 0 Jo

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Q: dx y In y || 2.

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Q: If 3x² + 2xy + y² = 2, then the value of dy/dx at x = 1 is

A: Given that        3x2+2xy+y2= 2 We have to find the value of dy/dx at x=1.

Q: If feF - dr = Sc(4x + 4y²) dx + (x²y) dy, what is.

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Q: Find dy/dx2 implicitly in terms of x and y. x*y – 6x = 9

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Q: -2y Six*y dx dy 3.

A: Given a double integral ∫12∫02yx3y dx dy we need to calculate This can be done as:

Q: Find d^2y/dx^2 for y=2x^3-5/x^2

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Q: if x3 + y3 =65, find the value of d2y/dx2 at the point (4,1)

A: Given that,    x3+y3=65

Q: d?y 7. y = e2" – 3e-, dx? dy - 2y = 0 dx

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Q: Find d^2y/dx^2 given 2xy-y^2=3.

A: Since we are given 2xy-y2=3 - (i)Our aim is to find d2ydx2 of equation (i) = ?

Q: If y=u³ and u = 4x² - 2x + 5, give dy dx

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Q: (3x'y +)dx + (2x'y-1)dy o

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Q: Solve for dy in the function dx Y= (3x-2)5(2x? +5)" and simplify the result.

A: The given function is y=3x-252x2+54

Q: c. (3xy3 + 4y)dx + (3x?y² + 2x)dy = 0; when x = 1, y = 1 %3D

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Q: by (3x? + y²) dx+ (2.xy) dy 7. C: 3D1 from (3,0) to (0,4) %3D - = 1 6.

A: We are given the following integral:∫C(3x2+y2) dx + (2xy) dy over the path C: x29+y216 = 1 from (3,…