What is the Analytical and Numerical Solution of the following First ODE's.
y^2 +x^2 y'=xyy'
You can get a solution in terms of elementary functions if you make y the independent variable:
y^2 dx + x^2 dy = x y dy
y^2 x'[y] + x[y]^2 == x[y] y In[5]:= DSolve[y^2 x'[y] + x[y]^2 == x[y] y, x[y], y] Out[5]= {{x[y] -> y/(C[1] + Log[y])}}
You can enter the equation into Wolfram|Alpha and it will tell you:
http://www.wolframalpha.com/input/?i=y%5E2+%2Bx%5E2+y%27%3Dxyy%27
The result appears using a function called "product log". You can learn more about the function in the documentation or online.
