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})

x \to 0 lim ((1 - 5 x)^{\frac{1}{x}})

\int tan (x) (sec (x))^{4} d x

\frac{d}{d x} (\frac{x ^{2}}{( x - 1 ) ^{2}})

\frac{d}{d x} (5 sec (x) tan (x))

u \to 8 lim (\frac{( u ^{2} - 5 u - 24 )}{u - 8})

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)