Find explicit solution, is this right?

[sumrtym77]

Explicit general solution of: yy'=x^2 (y^2 + 1)

y dy/dx = x^2 (y^2 + 1)

y/(y^2 + 1) dy/dx = x^2

integrate above and get: ln (y^2 + 1) / 2 = x^3/3 + c1

multiply both sides by 2: ln(y^2 + 1) = 2x^3 / 3 + 2c1

e both sides and get: (y^2 + 1) = e^(2x^3/3) + e^(2c1)

y^2 = e^(2x^3/3) + e^(2c1) - 1

y = sqrt (e^(2x^3/3) + e^(2c1) -1)

 

[royhaas]

Looks OK. You can re-write the last exression so that it shows only one constant, \(\displaystyle C = e^{2c1}-1\).