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

Question

5263 views around the world

You can reuse this answer
Creative Commons License

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:

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

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

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

$y = Csec(x)$

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