SOLUTION: Please help me solve this equation: Given that y = 0 when x = 1, solve the differential equation {{{ xydy/dx=y^2+4}}} obtaining an expression for y2 in terms of x.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me solve this equation: Given that y = 0 when x = 1, solve the differential equation {{{ xydy/dx=y^2+4}}} obtaining an expression for y2 in terms of x.      Log On


   

Question 860108: Please help me solve this equation: Given that y = 0 when x = 1, solve the differential equation +xydy%2Fdx=y%5E2%2B4
obtaining an expression for y2 in terms of x.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
xy%2A%28dy%2Fdx%29=y%5E2%2B4
%28y%2Ady%29%2F%28y%5E2%2B4%29=dx%2Fx
Substitute, u=y%5E2%2B4, du=2y%2Ady, %281%2F2%29du=y%2Ady
du%2F%282u%29=dx%2Fx
%281%2F2%29ln%28u%29=ln%28x%29%2BC
ln%28sqrt%28u%29%29=ln%28x%29%2BC
sqrt%28u%29=Cx
u=Cx%5E2
y%5E2%2B4=Cx%5E2
y%5E2=Cx%5E2-4
Solve for C.
0=C%281%29%5E2-4
C-4=0
C=4
highlight%28y%5E2=4%28x%5E2-1%29%29