What is the x*ln(x)=y(1+sqrt(3+y^2))y^'(x),y(1)=1 ?

The x*ln(x)=y(1+sqrt(3+y^2))y^'(x),y(1)=1 is y'(x)+y'(x)sqrt(3+y^2)

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

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

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

Solution steps

Find

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

given

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)

Expand

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

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

What is the x*ln(x)=y(1+sqrt(3+y^2))y^'(x),y(1)=1 ?
The x*ln(x)=y(1+sqrt(3+y^2))y^'(x),y(1)=1 is y'(x)+y'(x)sqrt(3+y^2)