What is a solution to the differential equation #dy/dx=12x^3y# with the particular solution #y(0)=2#?

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Answer 1 · 2017-02-14T10:07:28

#y(x) = 2e^(3x^4)#

This is a separable differential equation, so we can separate the variables and integrate:

#dy/dx =12x^3y#

#dy/y =12x^3dx#

#int dy/y = 12 int x^3dx#

#ln abs y = 3x^4 + C_1#

#y(x) = Ce^(3x^4)#

We can now determine the constant #C# from the initial condition:

#y(0) = 2#

#2 = Ce^0 = C#

so in conclusion:

#y(x) = 2e^(3x^4)#