2. Determine whether each of the following equations is exact. If exact, find the solutìon (you may leave your answer in implicit form): (a) ye"y + (2y xeªy' ) = 0 (b) 1+ In(xy) + xy¬!y' = 0

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 O B.…

A:

Q: Solve the following using exact equation or linear whichever is applicable. (2xy − 3x²) dx + (x² +…

A: We are given: (2xy − 3x²) dx + (x² + y) dy = 0⇒M=2xy − 3x²⇒N=x² + y ∂M∂y=2xand ∂N∂x=2x Hence, this…

Q: x*у + 2ху — у3 0, x>0

A:

Q: al solution to the following equation y"- y = 0

A:

Q: ( - 2 () 4 a) dx³ + yw = 0 dx, b) x(y")³ + (y')ª – y = 0 c) y = xy' + (y')² + 1

A:

Q: (6xty2) dx ty (2x-3y) dy = 0

A: To solve the given exact differential equation.6x+y2dx+y2x-3ydy=0

Q: 3. Prove that ox + 6x -4X12 is irreducible over Q.

A:

Q: Solve for the value of C in the equation: O A. 1 B. 2 (2xy¹ey + 2xy³ + y)dx + (x²y4eY − x²y² - 3x)dy…

A:

Q: = (9,4, 5) w = (10, 10, 10) Find the cosine of the angle between v and w. cos 0 =

A:

Q: Find all solutions between 0 and 2n for the following equation:

A:

Q: Find the general solution of the given equation y" + y = 0

A:

Q: Find all solutions of the form y = erx for the equation y''−y'−2y = 0. Then write the most general…

A: This is a second order differential equation. The solution of a second order differential equation…

Q: Find the general solution of the following equations in the standard form (ax + by = c). 1. (2x -…

A: We need to solve D.E.

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: Q 1. Solve the following simultaneous equations 2z+io=2 z+(1+i)@=3i

A: Write the second equation in terms of ω. z=3i-1+iω           ... 1

Q: Find the general solutions (implicit or explicit) to the following equations. (a) (x+y) dx – (x – y)…

A:

Q: -zy=0

A: Topic- Differential Equation

Q: Convert the given equation into the form of a Sturm-Liouville equation. y" +7y' + ay = 0 Write the…

A:

Q: Determine if y = ex is a solution to y′′′- 12y′′ + 48y′- 64y=0

A: y'= ex  y"= ex  y'"= ex

Q: Solve for the value of C in the equation: (3xy2 + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 O A. 4 B.…

A:

Q: Solve the following simultaneous equations 3z +io=1 z+(1-i)@=2

A:

Q: Find the general solution to the equation y4) – 6y" + 9y" = 0. NOTE: Use c1, c2, C3, and c, as…

A: We can rewrite the given equation as y''(y''-6y'+9y)=0 Put y = erx then y' = rerx and y'' = r2erx

Q: Find two solutions to 2y′′+ 5y′+ 2y= 0

A: for the homogeneous system, the auxiliary equation is given by

Q: xy" – y' + xy = 0, t =

A:

Q: Solve the given equation.. (3x?у +2ху + у?)аdx + (x2 + у?)dy %3D0 (3x?y+y)e3x = C (3x?y + y³)e3x = C…

A: Recall:  If the equation M(x,y)dx+N(x,y)dy=0 is not exact and ∂M∂y-∂N∂xN is a function of x…

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.