Differential Equations Answers

Equation in which M(x,y) and N(x,y) are Linear but not Homogeneous

Find the general solution of the following:

1.) (2x+3y-1)dx-4(x+1)dy=0

2.) (x-4y-3)dx-(x-6y-5)dy=0

(𝑡 +2)^2 𝑦′′ + (𝑡+2) 𝑦′ + 𝑦=0

Is y+P(x)y=Q(x)yⁿ a linear equation for integral value of n. Justify your answer.

Find the value of b for which the equation

(ye^2xy+x)dx +bxe^ 2xy dy= 0

How is a BVP different from IVP?

1.  dy/dt + ty=y ; y(1)=3

y′′−8y′+16y=24x+2

Instructions:

Good day! Equations are given below. Please determine which of the following equation is not a homogeneous equation. Thank you!

Choose the letter.

a. (y² - xy) dx + x²dy = 0

b. y' = 2xy e ^x/y / x²+y² sin(x/y)

Letter b is in fraction form.

c. 3x²ydx + (y+x³) dy = 0

d. 2x²y+3y³ (x³ + 2xy²) y' = 0

The population of a certain bacteria follows the logistic growth pattern. Initially, there are 10 gram of bacteria present in the culture. Two hours later, the culture weighs 25 g. The maximum weight of the culture is 100 g.

A. Write the corresponding logistic model for the bacterial growth.

B. What is the weight of the culture after 5 hours?

C. When will the culture's weight be 75 g?

HOMOGENEOUS EQUATION

Solve the given equation below. Show complete solution.

xy' = x + y