xln(x)=y(1+sqrt(3+y^2))y^'(x),y(1)=1

解

x ln (x) = y (1 + 3 + y^{2}) y^{^{'}} (x), y (1) = 1

y' (x) + y' (x) 3 + y^{2}

解答ステップ

以下の仮定で

y (1 + 3 + y^{2}) y^{'} (x)

を見つける:

y (1) = 1

y (1 + 3 + y^{2}) y^{^{'}} (x) = y (1 + 3 + y^{2}) y^{^{'}} (x)

y : 1

3 + y^{2} : 3 + 1^{2}

= 1 \cdot (1 + 3 + y^{2}) y^{^{'}} (x)

拡張

1 \cdot (1 + 3 + y^{2}) y^{'} (x) : y^{'} (x) + y^{'} (x) 3 + y^{2}

= y^{'} (x) + y^{'} (x) 3 + y^{2}