Describe two ways to find the general solution of (dy/dx) + 3xy = x. Verify that each method gives the same result.

Q: dy 4x2-х-2 : У(1) %3D 1 dx (х+1)(у+1)

A: Explained below

Q: ex dx /1-ex

A: Integration means addition it is used for adding continuous function which can't be added by simple…

Q: Solve this differenttial equation.   By help of integrating factor. (3xy+6y^2).dx+(2x^2+9xy).dy=0

A:

Q: solve using the appropriate method.

A:

Q: Solve each of the equations. Integrating Factors у (х + 2у + 2) dx + (2xу +5) dy %3D 0

A:

Q: Use the "integrating factor" method to solve the differential equation below. dy + 3x?y = -6x² dx |

A: We know that, the first order linear differential equation is given as dydx+Px·y=Qx           ⋯⋯1…

Q: Evaluate the following problems by obtaining the general solution. Show complete solution.…

A:

Q: 2) dy x+3y dx 2x

A: We will solve the problem

Q: In the case of a double integration, what changes if we change the order of integration? (Ex:…

A: we know the limits of integration the dx dy order and need to determine the limits of integration…

Q: PLEASE SHOW COMPLETE STEP-BY-STEP SOLUTION. Solve this First Order Linear DE dx/dt + (3/50+2t)x =…

A: In this question we will use basic of calculus i.e concept of solution of differential equations. We…

Q: 2. Solve the ff. equation using integrating factor. dy 2y – e3r dx

A: Given: dydx=2y-e3x

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

A:

Q: (2? + dy = 0 + In y) dx +

A:

Q: dy +y =2+2x dx

A:

Q: Solve the first order inhomogeneous equation dy + 2y = 3x2 dx Hint:

A:

Q: 2. Obtain the general solution using Bernoulli's equation. Simplify your final answer. + x dx - –…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve each of the equations. Integrating Factors (4x2 – 4x y + 3y² + 2) dx + x (2x – 2y + 1) dy = -

A: The differential equation given is as follows: 4x2-4xy+3y2+2dx+x2x-2y+1dy=0 We will check the…

Q: Find the general solution of the equation тx dy %3D пу dx

A: see calculation below

Q: dy _ y(ln(5y) – In(5x) + 3) dx 3x

A: The objective is to solve the differential equation dydx=yln5y-ln5x+33x Let, y=vx then dydx=v+xdvdx…

Q: 2. 2x5 = y(3x* + y²) %3D dx

A:

Q: Solve this DE:  1. dy/dx= (x+3y-2)2

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: I. Find the general solution of the following: 2x* 1. dx 2.d = xy 3. dy = (6e³x + 1)dx

A:

Q: dy = 6x– 2x + 1 cos y + eY %D dx

A:

Q: what is the general solution of a = e* dx +1

A:

Q: 4. x(xy – 1)dx + dy = 0(Non-exact)

A:

Q: Obtain the general solution unless otherwise instructed 1. arž -y = 10sin²x dx² SUMMARY OF ANSWERS…

A:

Q: 5. ye2*dx = (4+e2*)dy

A:

Q: Obtain the general solution using Bernoulli's equation. Simplify your final ansv answer. ix- 6* dy =…

A:

Q: Finally, we substitute for u to write the answer in terms of x. Use C for the constant of…

A:

Q: Solve dy/dx + 2y = 4, y(0) = 3 by one of the usual methods. Solve same the problem by Picard’s…

A: Integrating factor method for solving a differtial equation  Consider the differtial equation…

Q: Solve the equation (2х + 6) (2y? + 3) dx + 4y(x? + 3x + 2) dy %3D 0

A:

Q: Use an appropriate " Bernoulli substitution" to solve: dy + XY 4X s Y(O) =2. %3D dx ya

A: In order to solve a bernoulli's differential equation, first we have to convert it into a linear…

Q: Solve for the general solution * (eУ — усos ху) dx + (2xe-У — х соs ху +2у) dy %3D0

A:

Q: Use Picard’s Method with 3 iterations to solve for y(0.1) and y(0.2), the equation dy/dx = x2+y2;…

A: Picard method: Consider the initial value problem, dydx=fx, y, yx0=y0 Then  yn+1=y0+∫x0xfx,yndx…

Q: Find the solution of dy X. +y.Inx y.lny dx Show all your calculations.

A: Given equation is as below :

Q: dy dy dx dx 3.3

A:

Q: b) Find the general solution of (3sin y– 5x)dx+2x² cot ydy = 0

A:

Q: Solve using Bernoulli's Equation 1. x^2(dy/dx)+y^2=xy

A: We have to solve the given equation

Q: Check for exactness and obtain the general solution. 1. -x(4y3 – 3xy – 6)dx – (6x²y² + 1- x³)dy = 0

A:

Q: Solve the DE by Bernoulli's Equation 3 1.6 y² dx - x (2 x³+ y) dy = 0

A:

Q: ( 3х — у +1) dx- (9х- Зу — 3) dy %3D 0

A:

Q: Solve each of the equations. Integrating Factors Зу 3x?y + dx + (2.x + 6 In x) dy = 0 %3D

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution is: ∫Mdx⏟Take y…

Q: Determine the general solution for the following: 1. ( 6x2 - y +3 ) dx + (3y² -x - 2) dy =0

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Solve the Euler equation 2r dy 2.x dx? -3r given that y(1) =1 and y'(1) = 2. +3y 0 dx jntaios

A: To solve given differential equation first we write the auxiliary equation and find the roots and…

Q: (2xy - x + 2y - 1) dx + (8x² y² -2x + 4xy2 - x) dy = 0

A:

Q: dy 3. (а - by)у dx

A: Bernoulli's differential equation

Q: (2xy - x + 2y - 1) dx + (4x²y² - x² + 4xy² - x) dy = 0

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.