Differential Equations Answers

prove that the substitution u=y^1-n reduces the equation dy/dx+p(x)y=Q(x)yⁿ into a linear equation . hence solve the equation dy/dx+y/x=x/y³

using the method of variation of parameters to determine the solution to the equation

d²y/dx²-6dy/dx+9y=e^3x/x³

Determine the power series solution to the equation d²y/dx²+6xdy/dx-4y=0

about the point x₀=0

use the transformation x=e^t to transform the equation x²d²y/dx²-2xdy/dx+2y=x³ to a linear equation with constant coefficients hence solve the equation

use the laplace method to solve the equation

d²y/dx²+9y=9x y(0)=1 y'(0)=5

Find the eigen value and eigen function of homogeneous integral equation

y(x)= 𝜆"\\int"K(x,t)y(t)dt where K(x,t)= sinx sin(t-1) -𝜋<=x<=t

sint sin(x-1) t<=x<= 𝜋

Solve

"\\frac{dy}{dx}" =(x+2y-3)/(2x+y-3)

A certain particle falls under gravity in a resisting medium whose resistance varies with velocity.Find the relation between distance and velocity if the initially the particle starts from rest.