Differential Equations Answers

25y′′−70y′+49y=0Find the general solution of the differential equation 

(D²-2D+3)y=x²-1

The integrating factor of the given DE are already below. What is the value of "n".

(2y^2)dx-x((2x^3)+y)dy=0

IF=y^n

b. Find the series solution of the following differential equation

dz/dt -ze^t=tz

 w (4v + w) dv - 2 (v^2 - w) dw = 0

Use Laplace transform to solve initial value problem.

Y^2+Y={t,0 less than or equal to t less than 1

{0,t greater or equal to 1

y(0)=0,y'(0)=0

The differential equations dS/dt = -bSI+aS

dI/dt = bSI-cI

model a disease spread by contact, where S is the number of susceptibles, I is the number

of infectives, b is the contact rate, c is the removal rate and a is the birth rate of

susceptibles.

(i) Identify which term in the RHS of each differential equation arises from the birth of

susceptibles.

(ii) Discuss the model given by the above two differential equations.

d²y/dx² - dy/dx= e^-x , y(0) =0, y'(0) =1'

xzp - yzq= Kxyz by lagrange method

Non-exact equation and Integrating Factor

Given the equation below, solve for the general solutions.

w = dependent variable, v = independent variable

1. w(2v - w + 1) dv + v (3v - 4w + 3) dw = 0