SOLUTION: Solve the initial value problem yy′+x=√x^2+y^2 with y(1)=√3 a)To solve this, we should use the substitution u= My answer is y/x , wrong. u′= My answer is (xy'-y)/x^2 ,

Algebra ->  Exponents -> SOLUTION: Solve the initial value problem yy′+x=√x^2+y^2 with y(1)=√3 a)To solve this, we should use the substitution u= My answer is y/x , wrong. u′= My answer is (xy'-y)/x^2 ,      Log On


   



Question 1184060: Solve the initial value problem yy′+x=√x^2+y^2 with y(1)=√3
a)To solve this, we should use the substitution
u= My answer is y/x , wrong.
u′= My answer is (xy'-y)/x^2 , wrong.
Enter derivatives using prime notation (e.g., you would enter y′ for dy/dx).
b)After the substitution from the previous part, we obtain the following linear differential equation in x,u,u′.
My answer is xu'+u=(sqrt(1+u^2)-1)/u , wrong.
c)The solution to the original initial value problem is described by the following equation in x,y.
My answer is sqrt(x^2+y^2)-x=1 , wrong.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a) Use the substitution u+=+x%5E2+%2B+y%5E2. ===> u' = 2x + 2yy'

b) From (a), u'/2 = x + yy'. ===> u'/2 = sqrt%28u%29, or u' = 2sqrt%28u%29.

c) From (b), du%2Fdx+=+2sqrt%28u%29 ===> du%2Fsqrt%28u%29+=+2dx ===> 2sqrt%28u%29+=+2x+%2B+c

===> +2sqrt%28x%5E2+%2B+y%5E2%29=+2x+%2B+c. To get the value of c, plug in x = 1 and y=sqrt%283%29 into the equation.

===> 2sqrt%281%5E2%2Bsqrt%283%29%5E2%29+=+2+%2B+c ===> c+=+2, and
sqrt%28x%5E2%2By%5E2%29+=+x+%2B+1 is the solution to the BVP.