ii) x*(1-y³)dx+y(1+x³)dy=0

Q: d- . -x e-(x² +y²) dy dx -(x²+y²) dy dx

A: We can answer one question as per the honor policy. Please resubmit other question as well to know…

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: B: By using Homogenous method solve the first order differentia еquation (1+ e») dx - e"l> -1) dy =…

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Q: Only I method. Except Exact DE (x+2y-1)dx+(2x+4y-3)dy oo

A: First we campare the given differential equation Mdx+Ndy= 0 and then solve it.

Q: 2. [2x*tan y – ysin (2) – 1] dx + [xsin (2) + x*sec*y] dy =

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Q: 2- X %3D +2 3- Coshx dy +(y sinh x+e) dxo 36

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Q: Approximate - -1x+3 -dx using trapezoidal rule with n=4 and Simpson's rule with n=4.

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Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

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Q: 3. Differentiate y = 2x-1 - with respect to x and then evaluate 2 x(x – 1) -dx (2x – 1)2

A: Given and

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate (x' + 1)dx.

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Q: (2х — Зу)dx + (2у — Зx)dy %3D 0

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Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: 7. What is the order, degree and linearity of: (dy + 3x dx, d°x = ey dx3 8. What is the order,…

A: Note: since you posted multiple questions. As per our guidelines we are supposed to solve one…

Q: 14) find the respect of y with respect to x Y=(6x+5)^x dy/dx=?

A: Given function: y=6x+5x Taking log to the both sides logy=log6x+5x We know that logxa=a log(x) So,…

Q: 1- 2r (1 + y')dx - y (1 + 2x)dy =

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Q: (2siny + 1)dy : 4 and y(0) = 5. dx What is x when y = x?

A: Given:  2siny+1dydx=4, y0=π2 Using Variable separable  2siny+1dy=4dx Integrating both sides, we get…

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

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Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

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Q: •1 fl-x r4-x²-y 16. x dz dy dx 0 Jo 3

A: See the attachment

Q: Solve by integrating factors found by inspection: y (x2 - y2 + 1)dx - x (x2 - y2 - 1) dy = 0

A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

Q: 10. x = Vt-2, d²y y =t2-3' dx2

A: The given question is taken from the derivative and we have to find the derivative of the parametric…

Q: (a) --y = 2x?y, y(1) = 1 dy dx

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Q: (3 sin y – 5x)dx + 2x2 cot y dy = 0 -

A: Solution :-

Q: 2x dx by taking n = 4. 1+x Use trapezoidal Rule to evaluate

A: on solving this we get

Q: 2sin(y)cos(y) sint(y)+costy) dy

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Q: dy of y=X Find

A: y = x^x Find dy/dx

Q: (3 sin y – 5x)dx + 2x² cot y dy = 0

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

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Q: y= sinh-lx then prove that Vx2+1 dx

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Q: dy اذا كانت y = 3z2 + (sin(z وكان = *3ez؟ 4 : أحسب dx

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Q: 1. (2x -х-у)dx- хdy - 0; y(1) -о

A: Given that: (2x2-x-y)dx-xdy=0; y(1)=0

Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

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Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

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Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

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Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

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Q: 3) dy dx - y = sin x

A: We have to solve the given differential equation.   According to our guidelines we can solve only…

Q: 26. x = 2y, y(1) = 5 dy

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Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

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Q: 3. (2х - у - 4) dx - (х-3)dy -0 when x %3 1, y 3D 4.

A: We try to identify and group terms and integrate.

Q: dy for y = dx 9t -dt. 9t + 1 iz's rule to find

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Q: dy 1 (x³ + y²)Z dx 2

A: Given that The differential equation dydx=x3+y2 To apply uniqueness and existence theorem.

Q: y

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Q: xydy+(x^2-3y)dy=0

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Q: 2. メ +ッ 2. dy- X. dx

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Q: 9. 2y(у? — х)dy — dx, when x %3D2,у %3D 2

A: Given that: 9.     2y(y2-x)dy=dx,    when x=2, y=2     NOTE: As per our answering guidelines, we can…

Q: 9) (x- y°-Ay-1) dx t 2x (x4 y +2)dy =o

A: As we know that the differential equation Mdx+Ndy=0 is exact, If ∂M∂y=∂N∂x. The solution is:…

Q: Obtain the particular solution. 1. 2y dx = 3x dy ; when x = 2 , y = -1 .

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Q: .2 dy Find for y dx V6 – x5 - dy %3D dx

A: We have to find dydx

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.