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

Answered by Ryan S. Maths tutor

9648 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can I understand eigenvalues and eigenvectors?


Use the substitution u=x^2-2 to find the integral of (6x^3+4x)/sqrt( x^2-2)


Split (3x-4)/(x+2)(x-3) into partial fractions


Differentiate y=sin(x)/5x^3 with respect to x


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy