Use separation of variables to find an explicit solution. xyy' = 2xy² + y² %3D

Q: 4. If integration using u-substitution technique is used to solve for correct choice for u? (a) u =…

A:

Q: Obtain the solution using Integrating Factors Found by Inspection. 3.) 2x⁵y' = y(3x⁴ + y²)

A:

Q: (x2 + 3 y9 dx - 2xy dy

A: It is homogenous differential equation.

Q: 1. 2ydx + x (²+x²y) dy = 0

A:

Q: Use integrating factor to find the general solution of y' /(x2 +1) = 3 − xy

A: A first-order linear differential equation has a standard form of y'+P(x)y=Q(x). This differential…

Q: Find the particular solution of y (9x - 2y) dx -x (6x - y) dy=0., when x=1, y=1. Let x=vy

A:

Q: y" + y = sec x tan x

A:

Q: Use Euler’s method with the specified step size to estimate the value of the solution at the given…

A:

Q: (2х + Зу — 5)dx + (3х — у — 2)dy %3D0

A: The given differential equation is…

Q: dx dt -x + y + 2et ip dt — у — е-t

A: System of differential equation

Q: 1. Test for exactness and determine the particular solution of: (yexy – 2y³)dx + (xe*y – 6xy² –…

A:

Q: 2ydx + x(2 + x²y) dy = 0 %3D

A:

Q: x + 4) (y + 1)) dx + (y (x +3x + 2)) đy = 0

A:

Q: Obtain the solution using integrating factors found by inspection ydx + 2(y4-x)dy = 0

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

Q: Find a set of solution. Integrating factors found by inspection.   y(x2 + xy2 - 1) dx + x (x2 + y2…

A: Given the differential equation y(x2 + xy2 - 1) dx + x (x2 + y2 +1) dy =0. We need to find the set…

Q: y(x* – y²)dx + x(x* + y²)dy = 0

A: Let us consider the differential equation,  Where M and N are the function of  x and y. If the…

Q: y = 4xex

A:

Q: 2х + 3 d |(x² + 3x – 7)7 V

A: Given            ∫2x+3(x2+3x-7)7dx

Q: Solve by finding an integrating factor which has non-exact ODE and also find integrating factor from…

A: The differential equation is given as (xy2+y)dx-xdy = 0                        (1) Let the…

Q: Use Variation of Parameters to find a particular solution to the non-homogeneous equation y′′−2y′+y=…

A:

Q: otain the solution using Integrating Factors y(y+2x-2)dx - 2(x +y)dy = 0 %3D

A:

Q: Obtain the solution using Integrating Factors Found by Inspection. 1. ydx + 2(y* – x)dy = 0

A: As per our guidelines we can answer only 1 question. So kindly repost the remaining questions…

Q: Obtain the solution using Integrating Factors Found by Formulas. 2(2y2 + 5xy- 2y + 4)dx + x(2x +…

A: We can solve this using integrating factor

Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

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: Solve for the general solution of the given DE by using the integrating factors found by inspection.…

A:

Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* - х)dy %3D 0

A:

Q: 2x5y' = y(3x*+y?) %3D

A:

Q: xy' + y = sin(x), y(3) = 0, y'(3) = 0. Yh = C1x + c2x ln(x).

A:

Q: find a sets of solution. Integrating Factors found by inspection   x(x²−y² - x)dx− y(x²−y²)dy= 0…

A:

Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

A:

Q: y=Ax+Dx^B is the particular solution of the first-order homogeneous DEQ: (x-y) = 5xy'. Determine…

A: Given differential equation, 5xdydx=x-y,  x=3,y=6 dydx=x-y5x put, y=vx dydx=v+xdvdx now put values…

Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

A:

Q: 1. y(4x + y)dx – 2(x² – y)dy = 0

A: We will first convert the equation to exact and then solve

Q: Determine the integrating factor in the equation y(8x – 9y)dx + 2x(x – 3y)dy = 0 using the method of…

A: The given differential equation is  y8x-9ydx+2xx-3ydy=0 is of the form y f1x,y dx+x f2x,y dy=0. If…

Q: Obtain the general solution using separation of variables   y' = y sec x

A: Given: y'=y secx To Find: The general solution using separation of variables Concept:…

Q: exact method: (3xy3 + 4y)dx + (3x2y2 + 2x)dy = 0

A:

Q: Use Euler's method to estimate y(8) to estimate the solution to y' = y – 2x, y (0) = 1 %3D Use n = 4…

A: Given differential equation is y'=y-2x, y(0)=1.

Q: 4. x(x² – y² – x)dx – y(x² – y²)dy = 0, y(2) = 0

A: For the solution follow the next step.

Q: Use Euler's method to estimate y(0.02) ey-x y' = 1+e3y „y(0) = 4 0.01) What is the error in the…

A:

Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: 1. y(x³ – y)dx – x(x³ + y)dy = 0

A:

Q: (2у — Зx)dx + xdy 3D 0

A:

Q: Obtain the solution using Integrating Factors Found by Formulas. 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* – x)dy = 0

A:

Q: v(x² – y + x)dx + (x² – 2y) dy = 0 %3D

A: The given equation is 2yx2-y+xdx+x2-2ydy=0. Solve for the general solution using determination of…

Q: Find a solution for y' = y - y, y(0) = 0.2, h = 0.1 %3D using Modified Euler's Method. Hint: do 5…

A: Given that, y'=y-y2, y0=0.2, h=0.1

Q: Obtain the particular solution when x = 1 and y = 1 y(x^3-y^-5)dx-x(x^3+y^5)dy=0

A: Here is the solution of the given differential equation.

Q: Obtain the solution using Integrating Factors Found by Formulas 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +…

A: A detailed solution is given below.   (As per our guidelines, we have to solve only 1st question)

Q: y' = y sec

A:

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.