SOLUTION: Solve the Given Differential Equation by separation of variables. (dy)/(dx)=xsqrt(1-y^2) Answer: y=sin(x^2/2+c1) Please help me in providing step by step solution.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Solve the Given Differential Equation by separation of variables. (dy)/(dx)=xsqrt(1-y^2) Answer: y=sin(x^2/2+c1) Please help me in providing step by step solution.      Log On


   

Question 1143288: Solve the Given Differential Equation by separation of variables.
(dy)/(dx)=xsqrt(1-y^2)
Answer: y=sin(x^2/2+c1)
Please help me in providing step by step solution.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%28dy%29%2F%28dx%29=x%2Asqrt%281-y%5E2%29

Multiply both sides by dx

dy=x%2Asqrt%281-y%5E2%29dx

Divide both sides by sqrt%281-y%5E2%29

%28dy%29%2Fsqrt%281-y%5E2%29=x%2Adx

int%28+%28dy%29%2Fsqrt%281-y%5E2%29+%29%22%22=%22%22int%28x%2Adx%29

Use the formula: int%28%28du%29%2Fsqrt%28a%5E2-u%5E2%29%29%22%22=%22%22arcsin%28u%2Fa%29%2BC

arcsin%28y%2F1%29%22%22=%22%22x%5E2%2F2%5E%22%22%2BC

arcsin%28y%29%22%22=%22%22x%5E2%2F2%5E%22%22%2BC

Take the sine of both sides:

y%22%22=%22%22sin%28x%5E2%2F2%5E%22%22%2BC%29

Edwin