[The following initial value problem is defined with an exact differential equation. If the solution of this problem satisfies y(1) = B, evaluate 462 – 78 + a). S (8xy? + aa?y)da + (8y – 7æ)a'dy = 0, ly(-1) = 1. O-6 O-7 O-10 -8

Q: 1. (r - y2) dx = 2xy dy %3D

A:

Q: 3. Find the differential equation having the solution as of the following: a. y = c,e-x + cze-2x + x

A:

Q: Write a fifth-order differential equation that has the following general solution: Cез* + Сzе-2х +…

A:

Q: (x² + 2xy – 4y²) dx – (x² – 8xy – 4y²) dy = 0 - -

A: Consider a differential  equation M(x,y) dx+N(x,y) dy=0 then Check if the power of each term in…

Q: Given that Y1= cos(2x) and Y2 = sin(2X) are solutions for y+ 4y=0 find out which of the following is…

A: Explanation of the answer is as follows

Q: If B- 4AC = 0, then the general solution to the differential equation Ay+ By + Cy = 0 takes the form…

A:

Q: 2. The differential equation (x+1)y"+ay" =0 and the following data are assumed; 2 3 5 y 12 45 112…

A:

Q: A. Solve the following linear differential equation. 1. m*- 7m3 + 18m2 - 20m + 8 =0.

A: As per our norms we have to solve only one questions at a time kindly repost remaining questions.…

Q: Find the general solution to the following differential equation a. Xn+₁ = n +2 -X₁1 n +1 Xo = 1 2…

A: We need to find the general solution to the following differential equation. For (a), Given:…

Q: d²y dy 4х — + 6у — 4х — 3 dx | dx2

A:

Q: Solve the following differential equations (a) y/ = (b) = %3D ytev

A:

Q: d²y _ dy dx? --2y=0 dx

A:

Q: 3. Find the particular solution of the differential equation (y² – x²)dy – 2xydx = 0; when x = 4; y…

A: Given differential equation is y2-x2dx-2xydx=0                       (1) with condition , when x=4;…

Q: Use the method for solving equations of the form dy dx = G(ax + by) to solve the following…

A:

Q: 1. Solve the following differential equations and compare it to by-hand computation: a. y" - xy = 0

A: According to Bartleby guidelines I have solved first one. For remaining questions you can repost the…

Q: For which values of a and b is the following differential equation complete?…

A:

Q: Consider the following differential equation. 5x²y" + 4xy + 12x²y = 0

A:

Q: dy = (4x + y+1)? [Hint. Put 4x + y +1 = z] Ans. tan - 4x + y+1 2 2x+C d x

A: Variable separable form: Let us consider differential equation: dydx=f(x)g(y) g(y)dy=f(x)dx…

Q: Find the general solution of the differential equation 4xy - 1+ (3y +2x²) d=0 O +³² + 2yz² = c…

A: We have to find the general solution of the given differential equation.

Q: 5. Use the method of undetermined coefficients to solve the differential equation dy + a²y= cos bx,…

A:

Q: 1 10) y" +3y+2y = 1+e"

A:

Q: 3. Find the differential equation having the solution as of the following: a. y = ce-* + c2e¬2x + x…

A: The number of arbitrary constants in a given relation is the order of the differential equation of…

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.