Solving Differential Equations by Variation of Parameters

Determine the particular solution of the following nonhomogeneous differential equation using the method of variation of parameters y” + 4y’ + 4y = x^-2 e^-2x ; x>0 homogeneous equation is y =C1e^-2x +C2xe^-2x y= u1e^-2x +u2xe^-2x after differentiating and letting u’1e^-2x +u’2xe^-2x =0, we have _2u’e^-2x -2’u2xe^-2 ...continues

Solving Differential Equations by Variation of Parameters

Verify that e^x and x are solutions to the homogeneous equation corresponding to (1-x)y”+xy’-y=2(x-1)^2e^-x ; 0

Solving Bernoulli Equations

x*(dy/dx) + y = -2*x^6*y^4

Initial Value

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

Solving Differential Equations by Variation of Parameters

Verify that (1+x) and e^x are solutions to the homogeneous equation corresponding to xy'' -(1+x)y'+y=x^2 e^2x, x>0 and find the general solution. Book give an answer of Y(x)=1/2(x-1)e^2x

Radius of Convergence

Find the radius of convergence of About x= (-1/3) Thanks! Please see the attached file for the fully formatted problem.

Lower bound for the radius of convergence of the series.

Determine the lower bound for the radius of convergence of the series solution about x y’’ + 4y’ + 6xy = 0, x=1

Lower bound for the radius of convergence of the series.

Determine the lower bound for the radius of convergence of the series solution about x (x^2+1)y’’ + xy’ = 0, x=1

Mixture Problem as a Differential Equation.

Please solve using separation of variables method. A certain chemical is converted into another chemical by a chemical reaction. The rate at which the first chemical is converted is proportional to the amount of this chemical present at any instant. Ten percent of the original amount of the first chemical has been convert ...continues

Newton's Law of Cooling

Please explain any steps (separable, linear, etc) taken. Thank you. Assume Newton's Law of Cooling: A body cools from 60ºC to 50ºC in 15 minutes in air which is maintained at 30ºC. How long will it take this body to cool from 100ºC to 80ºC in air that is maintained at 50ºC?