Numerical and Analytical Solution of First ODE's

Questions
1

What is the Analytical and Numerical Solution of the following First ODE’s.

y^2 +x^2 y’=xyy’

2

You can enter the equation into Wolfram|Alpha and it will tell you:

The result appears using a function called “product log”. You can learn more about the function in the documentation or online.

3

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])}}