Check for exactness and solve (3.ry + y)dx +(x +.xy)dy = 0.

Q: dy 4. x - y = x² sin x dx

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Q: =x3 + y³ = 72, find the value of at the point (2,4). dx?

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Q: dy Using Bernoulli's equation, solve for the general solution of Please show complete dx 2x y…

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Q: particular solution (y-sqrt(x^2+y^2)dx-xdy=0 when x = 0 y = 1

A: The given differential equation is y-x2+y2dx-xdy=0. Solve the above equation as follows.…

Q: dy , 2xy - (1-x*)' . dx 1-x 2ху Solve

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Q: XY x + Vy² + 1 ) dx dy = 0 - Vy?+1

A: Topic  -  differential equation

Q: (xy² + y-x) dx + x(xy+1) dy = 0

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Q: dy Solve for the value of C in the equation: (1-2x)dx when y(0) - 1 3y3 3

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Q: dy + (2x – 3)y = x³ - dx Find the general solution.

A: Given: xdydx+2x-3y=x5

Q: Obtain the solution of the dy 1 1.x- + y = dx dy y2

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

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

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Q: Use separation of variable to solve and largest interval I over which the solution is defined. IV.…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: (x + у—4) dx — (х — у+2)dy %3D 0

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Q: Bernoulli's Equation 3dy – 4xy dx = 3x²y*e¬2x² dx 3x?y*e-2x? -

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Q: Q3. Solve dy (x+3) dx S 3x, 0 3.

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Q: Consider the equation, test whether it is exact and solve the IVP.        x(x-y)dy = y(y-3x)dx…

A: Solution:  Step I:    xx-y dy =yy-3xdx     y-1=1 Now,    xx-y dy=yy-3x  dx    dydx=yy-3xxx-y  Let…

Q: d²y Find the general solution for- dx² dx

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Q: Using undeterminate coefficien ts, Solve : d'y _q dy =9 e + 82* dx 3 3X 3 dx

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Q: cost, y = sint, at the point where t 0 ≤t≤ 2π -O?! =

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Q: I'Y (x) dx (x- 1)A =1+1+?. WINC

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Q: (1+ y²)dx + (x²y + y)dy = 0

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Q: Test the equation for exactness and solve the equation (2xy − 3x^2)dx + (x^2 + 2y)dy

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Q: 'ind the general solution and a particular solution by variation of param- y" + y = csc² (x)

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Q: d?y dy - 3- dx Determine the solution of x dx2

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Q: Solve using the method of variation of parameters: y" + 4y = sec X. %3D

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Q: 6. (2x + 3y)dx + (y- x)dy = 0 x)

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Q: Solve the equation 3(y+1)dx-(x+y+3)dy=0

A: Variable separable form of differential equation: dydx=f(x)g(y) Apply variable separable to given…

Q: (1 + y²) dx + (x²y + y) dy = 0.

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Q: z = xy dy x + y = 2x/1-x²y² 2. Using the substitution change the "dx to a separable equation. Hence…

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Q: Solve the differcential equation dy = xy - x, given that y = 2 when x = 0, expressing y in terms of…

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Q: A manufacturer can produce 5400 cell phones when x dollars is spent on labor and y dollars is spent…

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Q: ty" – (t+ 1)y' + y = t?

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Q: Solve f (5x + 6)eª dx using Integration by Parts. Use u = 5x + 6 and v' = e".

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Q: Find dy/dx: 1. y=x^2cos^4x I don't understand how to explain and solve

A: The given equation y = x^2cos^4x can be written as,

Q: dy Find the equation of the solution to dx x°y through the point (x, y) = (1, 2). help (equations)

A: We will find solution by using integration.

Q: Q5: Solve only one & explain your answer: xy-sinxcosx dy 1. dx %3D У(1-х2)

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Q: Solve the equation on the interval 0<0<2x. cot 0 + V3 = csc 0 %3D

A: cotθ+3=cscθ On simplification, we get…

Q: 3 I= |(e* +x² + A\dx Дх 3D0, 25 1

A: Solve the following

Q: Test the equation for exactness and if separable: (2xy + 2x) dx = y dy

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Q: By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

A: Consider the provided question, (b) (i)

Q: r1-x 2–2z 31. dy dz dx

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Q: Q2) Solve (y² + ysin x) dx – (cosx – 2xy +) dy = 0

A: If the equation is of form, Mdx+Ndy=0, then the equation is exact if ∂M∂y=∂N∂x. If the equation is…

Q: Classify then solve x(x - 1)dy - ((x-2)y + x*(2x- 1)) dx o

A: We will find out the required general solution.

Q: Exact equations (бх + у?)dx + yу(2ху — Зу?)dy %3D 0

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Q: If x+y = 63, find the value of dy at the point (-1,4). %3D dx2 The value of at the point (-1,4) is|:

A: Given, x3 +y3 = 63  We have to find the value of d2ydx2 at the point -1, 4.

Q: Q1- d?y Classify and Solve; dy = 0 dx dx2

A: Given: Differential equation is d2 yd x2 +dydx= 0 To classify and solve above differential equation…

Q: dy = a-x dx when x 1, y = 2 when x = 2, y = 0 %3D what is the value of a?

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Q: Q4 Find y'of y = In- %3D ? 1+e0

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Q: Classify and Solve dy + (1- 2x)y = 4x ,x >0 dx

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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.