Use any appropriate method to find the general solution of each of the following equations. dy - y² = yx + x² dx 3.2 3.

Q: Solve for the general solution of the given non-exact DE. y(2x + y?)dx + x(y² – x)dy = 0

A: The given differential equation:y2x+y2dx + xy2-xdy=0We need to solve the above equation.

Q: (x + y) dx + (3x + 3y - 4) dy = 0

A: given differential equation  x+ydx+3x+3y-4dy=0 solution let y+x=u differentiate dy=du-dx…

Q: Obtain the general solution of the following equations. 3. (4xy + 3y²)dx + x(x + 2y)dy = 0

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Q: 3. Show the equation (1+ e*y + xye*)dx + (xe* + 2)dy = 0 is exact and solve it.

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Q: B) Find the general solution of the equation by using (Undetermined Coefficients method) d'y dy de =…

A: Solution of the differential equation using undetermined method

Q: Find the general solution of the given Attached equation

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Q: Obtain the general solution to the equation. dy (x2 + 18) + xy - 6x = 0 dx The general solution is…

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Q: - x y² dx + e* dy = 0,y(0) = ; 2

A: Given differential equation xy2dx+exdy=0

Q: Find the general solution of the given Attached equation

A: Given: differential equation, To solve the differential equation first, substitute

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

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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: Obtain the general solution to the equation. dy_y dx + 4x + 9 X The general solution is y(x) =…

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Q: Find the solution to the Bernoulli equation: dy/dx + 2y/x = -x²y³

A: Introduction: One of the earliest differential equations to be solved was the Bernoulli equation,…

Q: Obtain the general solution to the equation. dy y dx = - + 5x + 6 X The general solution is y(x)=,…

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Q: -2y -2y (²²7) dx + e dy = 0 ex + x

A: Different ial eq is homogenous.

Q: Solve the following equation using Bernoulli D.E. b. Alternative method dy + 2 = y? dx 4.

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Q: (x + y) dx + (3x + 3y - 4) dy = 0

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Q: Solve the following Bernoulli equation: dy - 4y-2y dx

A: We have to do variable separation.

Q: (xy)dx + e*dy = 0, as xo, y =D;

A: Given:- (xy2) dx + ex dy=0 To find:- Particular solution of given differential equation

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: dy d. x = y + y³cosx dx е. dx - y = 2xy²e-*

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Q: Solve the following bernoulli equation dy/dx +y/x =xy^2

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Q: In each of the following, obtain the general solution. 1. (1-x)y' = y? 2. xy'dx + e*dy = 0

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Q: (8x² y² -2x + 4xy² - x) dx + (2xy + x + 2y + 1) 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: dy = 6x– 2x + 1 cos y + eY %D 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: 4. x(xy – 1)dx + dy = 0(Non-exact)

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

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

Q: S.2 „Determine whether the equation (3x + 2y)dx + (2x + y)dy = 0 is exact. Find the solution if it…

A: Given that  (3x+2y)dx+(2x+y)dy=0 To determine the general solution

Q: Obtain the general solution to the equation. dy y dx X + 9x + 7 The general solution is y(x)=,…

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Q: What is the general solution to the following equation: (dy/dx)= (y/x)+6x+1

A: Compare the given differential equation with standard form and calculate the integrating factor (IF)…

Q: Find the general solution of the following equations? 1- e* (y – x)dx + (1 + e*)dy = 0

A: To find the general solution ex(y-x)dx+(1+ex)dy=0

Q: Solve the following using the method of solving Bernoulli Equations. dy + y = e*y=2 dx

A: We need to solve the given differential equation by using Bernoulli's method.

Q: dy dy dx dx 3.3

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Q: Solve the exact equation   dy/dx= y/x

A: Given, dydx=yx

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 following non-exact equation: (3x'y + 2xy )dx +(2x'y' -x² )dy =0

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Q: find the general solution of the given equation. d2y/dx2 + 4 dy/dx + 4y = 0

A: d2ydx2+4dydx+4y=0 The auxiliary equation is, r2+4r+4=0⇒r+22=0⇒r=-2

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: find the general solution of the given equation. d2y/dx2 - 6 dy/dx + 9y = 0

A: Given: d2ydx2-6dydx+9y=0 Now plug dydx=D ⇒D2-6D+9y=0 Its auxiliary equation is,…

Q: 11. (x In y + xy) dx + (y In x + xy) dy = 0;

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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.