Solve the differential equation #dy/dx=ytan(x)#?

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Answer 1 · 2017-12-05T18:17:42

#y = Csec(x)#

Given: #dy/dx=ytan(x)#

Separate variables:

#dy/y = tan(x)dx#

Integrate both sides:

#intdy/y = inttan(x)dx#

#ln|y| = ln|sec(x)|+C#

Use the exponential function on both sides:

#e^(ln|y|) = e^(ln|sec(x)|+C)#

#e^(ln|y|) = e^Ce^(ln|sec(x)|)#

#e^(ln|y|) = Ce^(ln|sec(x)|)#

#y = Csec(x)#