Homework Help

Solve the differential equation dy/dx=8x^2y^2 with the condition given  that y(2)=3 .

user profile pic

barce90 | Student, Undergraduate | Honors

Posted May 9, 2013 at 3:36 AM via web

dislike 1 like

Solve the differential equation

dy/dx=8x^2y^2 with the condition given  that y(2)=3 .

2 Answers | Add Yours

user profile pic

pramodpandey | College Teacher | Valedictorian

Posted May 9, 2013 at 4:22 AM (Answer #1)

dislike 0 like

We have given

`(dy)/(dx)=8x^2y^2`

In the problem ,variables are separable. Thus

`(dy)/y^2=8x^2dx`

Integrating, we have

`int(dy)/y^2=8intx^2dx+c`

`y^(-2+1)/(-1)=8x^(2+1)/3+c`

`-y^(-1)=(8/3)x^3+c`

Given x=2,y=3 ,thus

`-3^(-1)=(8/3)(2)^3+c`

`c=64/3+1/3=65/3`

`y^(-1)=-{65/3+(8/3)x^3)`

`y=-1/{(65/3)+(8/3)x^3}`

user profile pic

barce90 | Student, Undergraduate | Honors

Posted May 10, 2013 at 3:56 AM (Answer #2)

dislike 0 like

dy/dx=16xy^2/8x^2y, but now with the condition that y(2)=3 what would be the answer then?

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes