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# Solve the differential equation du/dt = (5 + t^{4}) / (ut^{2} + u^{4}t^{2})

**Solution:**

This differential equation can be solved by variable separable method.

A differential equation is said to be in variable separable form if it can be represented in the form,

f(x)dx = g(y)dy

Given, du/dt = (5 + t^{4})/ (ut^{2} + u^{4}t^{2})

du/dt = (5 + t^{4})/ t^{2}(u + u^{4})

Sorting like terms,

(u + u^{4}) du = (5 + t^{4})/ t^{2} .dt

(u + u^{4}) du = (5t - 2 + t^{2}) dt

Integrating on both sides,

∫(u + u^{4}) du = ∫(5t - 2 + t^{2}) dt

u^{2 }/ 2 + u^{5 }/ 5 = 5t^{2}- 2t+ t^{3}/ 3 + C

## Solve the differential equation du/dt = (5 + t^{4}) / (ut^{2} + u^{4}t^{2})

**Summary:**

The solution for the differential equation du/dt = (5 + t^{4}) / (ut^{2} + u^{4}t^{2}) is u^{2 }/ 2 + u^{5 }/ 5 = 5t^{2 }-2t + t^{3 }/ 3 + C.

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