Differential Equations Answers

Solve the differential equation (x +4) dy/dx = x(y-3), given that y=4 when x= -3.

Given that y_1 = e^{x}

y1 =e^x

is a solution of xy’’+(1-2x)y’+(x-1)y=0

xy’’+(1−2x)y’+(x−1)y=0, find its second solution y_2

y2

(0,∞), which is linearly independent from y1

Use any appropriate method in finding the indicated solution of the following differential 

equations. 

[2𝑥𝑦 cos(𝑥2) − 2𝑥𝑦 + 1]𝑑𝑥 + [𝑠𝑖𝑛(𝑥2) − 𝑥2]𝑑𝑦 = 0

Find the particular solution of the equation

e^2tdy/dx=4

Given that y=5, t=0

Find the particular solution for the following equation y"-y'-12y=te^4t

Find the linear and Bernoulli’s differential equations from the following differential equations and solve it.i)(1-x^2)dy/dx-xy=1 ii)dy/dx=xy^2-xy

Find the general solution of the given differential equation.

(x + 1) dy/dx + (x + 2)y = 2xe^−x

Let P(t) be the population of a certain animal species. Assume the

P(t) satisfies the logistic growth equation,

dP

dt = 0.2P(t) (1 −

P(t)

200) , y(0) = 150

a) Is the above equation autonomous? if yes (explain your answer with

proper reasons), if no (justify you answer).

b) Solve the above initial value problem, and find the value of solution at

time t = 0.5 using separation of variables

Consider the autonomous DE xʹ = x(x − 1)(x+ 2). Determine the

critical points of the equation. Discuss a way of obtaining a phase portrait

of the equation.