solving \(\displaystyle{y}{''}+{y}={\sec{{\left({x}\right)}}}\)

acidizihvzs

acidizihvzs

Answered question

2022-04-02

solving y+y=sec(x)

Answer & Explanation

kachnaemra

kachnaemra

Beginner2022-04-03Added 16 answers

y+y=sec(x)
ycos(x)ysin(x)+ysin(x)+ycos(x)=1
ycos(x)+ysin(x)=x+K
(ycos(x))=x+Kcos2(x)
(ycos(x))=x+Kcos2(x)dx
y(x)=cos(x)xcos2(x)dx+K1sin(x)+K2cos(x)
y(x)=cos(x)(xtan(x)+ln(cos(x)))+K1sin(x)+K2cos(x)
y(x)=xsin(x)+cos(x)ln(cos(x))+K1sin(x)+K2cos(x)
Maybe the method with variation of constant will work with a correct substitution first

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?