Solve the differential equation: dy/dx = tan^3(x)sec^2(x)

dy/dx = tan3(x)sec2(x)

Integrate both sides ==> ∫dy= ∫ tan3(x)sec2(x) dx

Use the substitution u=tan(x)

And by differentiation du/dx = sec2(x) , which leads to dx = du/sec2(x)

==> and subbing dx into the equation leads to the simplification of y = ∫ u3 du

Integrate with respect to u to get y = u4/4 + c

Then sub u back into the equation to find y = tan4(x) + c

RS
Answered by Ryan S. Maths tutor

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