Asked by milli
                Part 1) Find the general solution of the differential equation dy/dx + 4xy^6 = 0
Option 1) . y(x) = (A + 10x^2)^-1/5
Option 2) y(x) = (A - 12x^2)^-1/6
Option 3) y(x) = (A + 12x^2)^1/6
Option 4) y(x) = (A - 10x^2)^-1/5
Option 5) y(x) = (A + 10x^2)^-1/6
Part 2) Find the particular solution y0 such that y0(0) = 1/2
Option 1) y0(x) = (32 + 12x^2)^1/5
Option 2) y0(x) = (64 - 12x^2)^1/6
Option 3) y0(x) = (64 + 12x^2)^-1/6
Option 4) y0(x) = (32 + 10x^2)^-1/5
Option 5) y0(x) = (32 - 10x^2)^-1/5
Part 3) For the particular solution y0 in (ii), find the value of y0(1)
Option 1) 77^1/6
Option 2) 44^-1/5
Option 3) 76^1/6
Option 4) 43^1/5
Option 5) 42^-1/5
            
        Option 1) . y(x) = (A + 10x^2)^-1/5
Option 2) y(x) = (A - 12x^2)^-1/6
Option 3) y(x) = (A + 12x^2)^1/6
Option 4) y(x) = (A - 10x^2)^-1/5
Option 5) y(x) = (A + 10x^2)^-1/6
Part 2) Find the particular solution y0 such that y0(0) = 1/2
Option 1) y0(x) = (32 + 12x^2)^1/5
Option 2) y0(x) = (64 - 12x^2)^1/6
Option 3) y0(x) = (64 + 12x^2)^-1/6
Option 4) y0(x) = (32 + 10x^2)^-1/5
Option 5) y0(x) = (32 - 10x^2)^-1/5
Part 3) For the particular solution y0 in (ii), find the value of y0(1)
Option 1) 77^1/6
Option 2) 44^-1/5
Option 3) 76^1/6
Option 4) 43^1/5
Option 5) 42^-1/5
Answers
                    Answered by
            oobleck
            
    dy/dx + 4xy^6 = 0
dy/dx = -4xy^6
y^-6 dy = -4x dx
-1/5 y^-5 = -2x^2 + C
or
y^5 = 10x^2 + C
Now use y(0) = 1/2 to find C, and
then find y(1)
    
dy/dx = -4xy^6
y^-6 dy = -4x dx
-1/5 y^-5 = -2x^2 + C
or
y^5 = 10x^2 + C
Now use y(0) = 1/2 to find C, and
then find y(1)
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.