3. $$\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { 2 } - y ^ { 2 } , \quad y = 1 \text { at } x = 0 \text {. (I) }$$ (b) By differentiating (I) twice with respect to \(x\), show that $$\frac { \mathrm { d } ^ { 3 } y } { \mathrm {~d} x ^ { 3 } } + 2 y \frac { \mathrm {~d} ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 2 \left( \frac { \mathrm {~d} y } { \mathrm {~d} x } \right) ^ { 2 } - 2 = 0$$ (c) Hence, for (I), find the series solution for \(\boldsymbol { y }\) in ascending powers of \(\boldsymbol { x }\) up to and including the term in \(\boldsymbol { x } ^ { \mathbf { 3 } }\). (4)