What is the solution for (t^2+16)((dx)/(dt))=(x^2+25),x(0)=5 ?

The solution for (t^2+16)((dx)/(dt))=(x^2+25),x(0)=5 is x=5tan((5arctan(t/4)+pi)/4)

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(t^2+16)((dx)/(dt))=(x^2+25),x(0)=5

(t^{2} + 16) (\frac{d x}{d t}) = (x^{2} + 25), x (0) = 5

x = 5 tan (\frac{5 arctan ( \frac{t}{4} ) + π}{4})

Solution steps

(t^{2} + 16) (\frac{d x}{d t}) = (x^{2} + 25)

Solve separable ODE:

x = 5 tan (\frac{5 arctan ( \frac{t}{4} ) + π}{4})

x = 5 tan (\frac{5 arctan ( \frac{t}{4} ) + π}{4})

What is the solution for (t^2+16)((dx)/(dt))=(x^2+25),x(0)=5 ?
The solution for (t^2+16)((dx)/(dt))=(x^2+25),x(0)=5 is x=5tan((5arctan(t/4)+pi)/4)