Solve dy/dx+1=e^x+y 🤔 Differential Equation | Integrating factor method

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Solve the differential equation dy/dx+1=e^x+y by using the integrating factor method.
How to solve first-order linear ordinary differential equation?

Strategy of solving differential equations using integrating factor method:
1. Write the differential equation in the from dy/dx+P(x)y=Q(x).
2. Obtain P(x) then integrate.
3. Calculate the integrating factor, ρ=e∫P(x)dx.
4. Rewrite the differential equation in the form of d/dx ρy=ρQ(x)
5. Integrate both sides with respect to x.

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