Find the solution of the differential equation dy/dx = y^2/x^4 that satisfies the initial condition y(1) = 1?

Question

3645 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-24T07:56:25

#y = (3 x^3)/(1 + 2 x^3)#

#dy/dx = y^2/x^4# is separable as follows:

#dy/y^2 = dx/x^4#

Integrating:

#- 1/y = - 1/(3x^3) + C# or #1/y = 1/(3x^3) + C#

Applying IV: #qquad y(1) = 1#

#1/1 = 1/(3(1)^3) + C implies C = 2/3 #

#1/y = 1/(3x^3) + 2/3 = (1 + 2 x^3)/(3 x^3)#

#implies y = (3 x^3)/(1 + 2 x^3)#