Question #b8c93

2 Answers
May 10, 2017

#y = Ce^(-x^2) + 2#

Explanation:

Given: #dy/dx+2xy=4x#

Subtract #2xy# from both sides:

#dy/dx = 4x-2xy

Factor:

#dy/dx = -2x(y-2)#

This is a separable equation:

#dy/(y-2) = -2xdx#

After integration:

#ln|y-2| = -x^2+C#

Make both sides exponents of e:

#y -2 = Ce^(-x^2)#

Add 2 to both sides:

#y = Ce^(-x^2) + 2#

May 10, 2017

The solution is #y=2+C_1e^(-x^2)#

Explanation:

This is first order differential equation with separable variables

#dy/dx+2xy=4x#

#dy/dx=4x-2xy=-2x(y-2)#

#dy/(y-2)=-2xdx#

#intdy/(y-2)=-int2xdx#

#-ln(y-2)=-2x^2/2+C#

#ln(y-2)=-x^2+C#

#y-2=C_1e^(-x^2)#

#y=2+C_1e^(-x^2)#