What is the xln(x)=y(1+sqrt(15+y^2))y^'(x),y(1)=1 ?

The xln(x)=y(1+sqrt(15+y^2))y^'(x),y(1)=1 is y'(x)+y'(x)sqrt(15+y^2)

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xln(x)=y(1+sqrt(15+y^2))y^'(x),y(1)=1

x ln (x) = y (1 + 15 + y^{2}) y^{^{'}} (x), y (1) = 1

y' (x) + y' (x) 15 + y^{2}

Solution steps

Find

y (1 + 15 + y^{2}) y^{'} (x)

given

y (1) = 1

y (1 + 15 + y^{2}) y^{^{'}} (x) = y (1 + 15 + y^{2}) y^{^{'}} (x)

y : 1

15 + y^{2} : 15 + 1^{2}

= 1 \cdot (1 + 15 + y^{2}) y^{^{'}} (x)

Expand

1 \cdot (1 + 15 + y^{2}) y^{'} (x) : y^{'} (x) + y^{'} (x) 15 + y^{2}

= y^{'} (x) + y^{'} (x) 15 + y^{2}

\int e^{12 x} \cdot x^{3} d x

x \to - 4 lim (x^{3} - 4 x^{2} + 7)

3 y^{^{''}} - 12 y^{^{'}} + 9 y = 3 sin (4 x)

x \to 1 lim (\frac{x}{( x - 1 ) ^{2}})

y^{^{'''}} - y^{^{'}} = 2 sin (3 x)

What is the xln(x)=y(1+sqrt(15+y^2))y^'(x),y(1)=1 ?
The xln(x)=y(1+sqrt(15+y^2))y^'(x),y(1)=1 is y'(x)+y'(x)sqrt(15+y^2)