Unformatted text preview: f x = ( x1 + x2 y 3 ) and integrating by x , we get f ( x,y ) = log xx1 y 3 + φ ( y ) . Diﬀerentiating by y , we have f y =3 x1 y 2 + φ ( y ), which must equal3 x1 y 2 . Hence we must have φ ( y ) = 0, so we can take φ ( y ) = 0. The solution to the diﬀerential equation is simply f ( x,y ) = C , so log xx1 y 3 = C. Using the initial condition y (1) = 8, we have8 3 = C , so the solution to the initial value problem is log xx1 y 3 =8 3 . 1...
View
Full Document
 Spring '07
 staff
 Math, Boundary value problem, x1 + x2

Click to edit the document details