What is the solution for x^'=x^2+1/36 ,x(0)=7 ?

The solution for x^'=x^2+1/36 ,x(0)=7 is x=(tan((t+6*1.54699…)/6))/(6)

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x^'=x^2+1/36 ,x(0)=7

x^{^{'}} = x^{2} + \frac{1}{36}, x (0) = 7

x = \frac{tan ( \frac{t + 6 \cdot 1.54699 \dots}{6} )}{6}

Solution steps

x^{'} (t) = x^{2} + \frac{1}{36}

Solve separable ODE:

x = \frac{tan ( \frac{t + 6 \cdot 1.54699 \dots}{6} )}{6}

x = \frac{tan ( \frac{t + 6 \cdot 1.54699 \dots}{6} )}{6}

\frac{d y}{d x} + 5 x y = 8 x, y (0) = 2

y^{^{'}} = - \frac{2 y}{100 + 2 t}

y^{^{'}} = (1 - y) \cdot (2 - y)

\frac{4 d y}{( x ^{2} + 1 d x )} = \frac{1}{2 y}

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

What is the solution for x^'=x^2+1/36 ,x(0)=7 ?
The solution for x^'=x^2+1/36 ,x(0)=7 is x=(tan((t+6*1.54699…)/6))/(6)