What is the xln(x)=y(1+sqrt(8+y^2))y^'(x),y(1)=1 ?

The xln(x)=y(1+sqrt(8+y^2))y^'(x),y(1)=1 is y'(x)+y'(x)sqrt(8+y^2)

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xln(x)=y(1+sqrt(8+y^2))y^'(x),y(1)=1

x ln (x) = y (1 + 8 + y^{2}) y^{^{'}} (x), y (1) = 1

y' (x) + y' (x) 8 + y^{2}

Solution steps

Find

y (1 + 8 + y^{2}) y^{'} (x)

given

y (1) = 1

y (1 + 8 + y^{2}) y^{^{'}} (x) = y (1 + 8 + y^{2}) y^{^{'}} (x)

y : 1

8 + y^{2} : 8 + 1^{2}

= 1 \cdot (1 + 8 + y^{2}) y^{^{'}} (x)

Expand

1 \cdot (1 + 8 + y^{2}) y^{'} (x) : y^{'} (x) + y^{'} (x) 8 + y^{2}

= y^{'} (x) + y^{'} (x) 8 + y^{2}

\frac{d}{d x} (in (x^{2} + 1))

\frac{d y}{d x} = y^{2} + 1

\frac{d}{d x} (e^{\frac{- x ^{2}}{8}})

\int (ln (x))^{4} \frac{1}{x} d x

\int_{3}^{4} \frac{x}{x ^{2} - 1} d x

What is the xln(x)=y(1+sqrt(8+y^2))y^'(x),y(1)=1 ?
The xln(x)=y(1+sqrt(8+y^2))y^'(x),y(1)=1 is y'(x)+y'(x)sqrt(8+y^2)