3. Solve the initial-value problem: 2 dy = 2xy + 3y y(1) = dx 1

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

A: To solve the IVP: dydx=2x+12y, where y-2=-1. Solution: Separating the variables of the given…

Q: 5. Solve (y² + 3xy³) dx + (1 - xy)dy = 0.

A:

Q: 3.2 (2x - y²) dxdy

A:

Q: Solve for DE (x + 2y - 3)dx - (2x + 4y - 9) dy = 0

A: In this question,  we solve given DE by substitution methode i. e.  We put some terms in the form of…

Q: solve D.E. by using Linear (y? + 1)dx + (2xy+ 1)dy= 0

A: See the attachment

Q: 4. Solve dy d.x. 3y² - x² XU . Note: your solution may be left in implicit form.

A: Use variable separation method after y substitution to solve.

Q: 6. Solve the initial value problem: dx (x² + 2y²). = xy, y(-1) = 1 dy %3|

A: First of all write the given initial value problem in MDX+Ndy=0 form which is the homogeneous…

Q: Solve (x − y − 1) dy − (x + 3x − 5) dx = 0

A: Rewrite the differential equation as                 dydx=x+3y-5x-y-1

Q: Find d2y/dx2 for the equation x=x3y2-3y3

A:

Q: Solve (yz + хуz) dx + (zx + хуz) dy + (ху + хуz) dz =

A:

Q: Solve the following D.Es: 1. (x+ 1) = x(y² + 1). dr

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

Q: Solve (2x – 1)3y" + (2x – 1)y' - 2y = 8x? – 2x + 3 %3D |

A:

Q: (b) Solve the IVP (3xy – y²)dx = (xy – x²)dy y(-2) = 3 - %3D %3D

A:

Q: The solution of (xy – ) = y³e-x² dx

A: The solution of the differential equation is defined as the function that satisfies the equation.…

Q: If dy/dx = 4x/y and y(0) = 5, find an equation for y in terms of x. A x²/2=2y² + 25/2 B. y²/2 =…

A: To solve the following problem

Q: 1. Find the solution of +=3x ; y(2)=3. dx 4x

A: we have to find the solution dydx+y4x=3x ;  y(2)=3

Q: Solve the following initial value problem (y)dx+(y4-4x)dy=0 with x(2)=5/2.  For your final answer,…

A: Given,      (y)dx+(y4-4x)dy=0  and   x2=52

Q: 5. Implicitly differentiate the equation (xy)-y=x to find dx

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.