Calculus, EXT1 EQ-Bank 22 Solve the differential equation \(\dfrac{d y}{d x}=20 e^{-5 y}\). (3 marks) --- 8 WORK AREA LINES (style=blank) --- Show Answers Only \(y=\dfrac{1}{5} \ln \abs{100 x+c}\) Show Worked Solution \(\dfrac{d y}{d x}\) \(=20 e^{-5 y}\) \(\displaystyle \int e^{5y}\,d y\) \(=\displaystyle \int 20\, d x\) \(\dfrac{1}{5} e^{5 y}\) \(=20 x+c\) \(e^{5 y}\) \(=100 x+c\) \(5 y\) \(=\ln \abs{100 x+c}\) \( y\) \(=\dfrac{1}{5} \ln \abs{100 x+c}\)