3y(x² – 1)dx + (x³ + 8y – 3x)dy = 0; when x O and y = 1.

Q: Solve the following Bernoulli Equations. (show complete solutions) a.) (3x - 2y + 1)dx + (3x - 2y +…

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Q: 2) Determine the constant A such that the equation (x² + 12ry) dx – (Ar² + 8y) dy = 0 is exact and…

A: The differential equation P(x,y)dx+ Q(x,y)dy =0 is an exact equation if and only if…

Q: . Solve the following Ricatti equations: 2 y - y² = -x², given that y₁ = x² is a particular dy dx…

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Find all values of the constant c so that .2 (xy + 1)dy dx = 4 + 4c.

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Q: How can we solve this separable equation? N(y) * dy/dx = M(x)

A: The given differential equation is, Where, N(y) and M(x) are the functions of the variable y alone…

Q: Use any appropriate method to find the general solution of each of the following equations. dy - y²…

A: Given differential equation is, x2dydx-y2=yx+x2

Q: Solve the following by Substitution Method. (show complete solutions) a.) y(x tanx + ln y)dx + tanx…

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Q: Use appropriate substitution to reduce the following equation to a variable separable and then dy 3x…

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Q: Q6) Solve the following DE: dy -5y 0 dx

A: Given : dydx-5y= 0 Now, 1ydydx = 5

Q: Solve the following equation and show that it is exact 3x (xy +2)dx + (x^3 - 2y)dy = 0

A: Given differential equation is  3x(xy+2)dx+(x3-2y)dy=0

Q: d.) (y³ + x ln ) dy + (y In ) dx = 0

A: we have to find

Q: Find the general solution of the D.E (D^2+4)y=sin3x

A: We have to solve the problem

Q: Q5) Answer the Following: 1- Solve the separable DE: dy -x² dx y² A a gortain

A: Given differential equation : dydx=-x2y2

Q: (2y² + 3xy – 2y + 6x)dx + x(x + 2y – 1)dy = 0

A: The differential equation is given as (2y2+3xy-2y+6x)dx+x(x+2y-1)dy=0 Let the integrating factor be…

Q: -2y -2y (²²7) dx + e dy = 0 ex + x

A: Different ial eq is homogenous.

Q: 6. Solve the D.E. 2y" + 18y = tan(3x). %3D

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Q: dx + (х-1) {In(2x – 2) +dy = 0 2. Test for exactness and find the complete solution of

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Q: (Zy+3)2 a. dx (4x+5/

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Q: Use appropriate substitution to reduce the following equation to a variable separable and then Зх +…

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Q: dy 1. 6x², y(0)=5 || dx dy 2. dx e* +4 e* y(0)= In 5 '

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Solve for linear but not homogenous equation and find the general solution of each of the following:…

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Q: From the following equations select the one that is not exact and solve. (x2- у) dx — х dy%3D0 1.…

A: A differential equation of the form Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x 1)…

Q: Find the general solution of a given non exact DE y(8x-9y)dx+2x(x-3y)dy=D0. (Note: Express your…

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Q: Find the general solution of the following Differenti 1. y(y2 + 1)dx + x(y² – 1)dy = 0

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Q: SOve the exact DE and Give the general Solution. ay-3x)y'-3y=D0

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Q: (1 + y²) dx + (x²y + y) dy = 0.

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Q: Solve for the solution for the equation: (x² + 3xy)dx + (x² + 4y) dy = 0 with the condition of y(2)…

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Q: Solve the general solution of the given DE:(2r+y)dx-xdy=D0*

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Q: 12. Solve the following first-order equations: dy а. = 4x/y, with y(0) = 1 %3D dx

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Q: d³y d?y dy dx3 dx3 - y = 4 sin x dx

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Q: find a set of solutions unless the statement of the exercise stipulates otherwise use any method in…

A: Let us consider the differential equation M(x,y)dx+N(x,y)dy=0 Now, if ∂M∂y=∂N∂x that is if the…

Q: Solve the following equations= dy (x² Jy 1- dx

A: I have stated the used formula in the solution.

Q: Solve the given IVP. x²° = y² + xy y(1) = 1 %3D dx Hint: Use substitution to change the equation to…

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Q: Q1:- Solve the following DEs:- (-4y + e-3*)dx = 4 dy %3D

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Q: The µ(x) that converts the equation below into an exact equation x dy (x*ev ++ (2x²e" + 1) = 0 y) dx…

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Q: Q21// find the general solution (sin²x + 2ye²x + 2)dx + (e2x – sec²y) dy = 0

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Q: Obtain the general solution to the equation. dy + 9x +8 - dx The general solution is y(x) = ,…

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Q: Find the general solution of the equations given below: dy i) 4 - y = x² – 3x; dx2

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Q: 35. Find a value of the constant k so that kx²y dx dy = 1.

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Q: 3. Choose one of the following first-order equations to solve. dy (x² + 1): + 3x(y – 1) = 0 dx а. %D

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Q: Solve the diffrential equation.(pls step bu step and clearly) (d/dx+2x)(dy/dx+2xy)=2e^(-x^2)

A: We have given differential equation is…

Q: d^2y/dx^2 + 3dy/dx + 4y = 3x + 2 Utilize the indeterminate coefficient technique to solve the above…

A: Here is the, solution

Q: 1 and write the new equation in the form A+B÷ xy3 dy = 0. dx b) Multiply the equation with u = Show…

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Q: (3x'у — х?) dx + dy -0 а. b. dx – 2xy dy = 0

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Q: Solve the following Bernoulli equation: dy - = 4y-2 y² dx 1 y = B A 1 y = Ce 4 В A B y =Ce¯4* + A A…

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Q: (ylny – e¯xy)dx + ( + xlny) dy = 0

A: Solution :-

Q: Solve the following equation to obtain the family of solutions.Show your solution. (2x³-xy²-2y+3)dx…

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Q: Q1) Solve the following equation with Bern dy X - dx + y = 3x³y3

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Q: II. Determine the solutions of the following DE. 1. (х — Зу + 2)dx + 3(x + 3у — 4)dy %3D0

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

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.