Solve differential equation y'+y=x, \ y(0)=1

Question
Solve differential equation \(\displaystyle{y}'+{y}={x},\ {y}{\left({0}\right)}={1}\)

Answers (1)

2021-03-09
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{d}{n}}}}+{y}={x}\)
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{d}{n}}}}+{p}{y}={x}\)
\(\displaystyle{I}.{F}.={e}^{{\int{p}{\left.{d}{x}\right.}}}={e}^{{\int{1}{\left.{d}{x}\right.}}}={e}^{{x}}\)
\(\displaystyle{y}{\left({I}.{F}.\right)}=\int{0}{\left.{d}{x}\right.}+{c}\)
\(\displaystyle{e}^{{n}}{y}={\frac{{{x}^{{2}}}}{{{2}}}}+{c}\)
c=1
\(\displaystyle{y}={\frac{{{x}^{{2}}}}{{{2}}}}{e}^{{-{n}}}+{e}^{{-{x}}}\)
0

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