Calculus, EXT1 EQ-Bank 13 Solve the differential equation \(\dfrac{d y}{d x}=3 y\). (3 marks) --- 7 WORK AREA LINES (style=lined) --- Show Answers Only \(y=e^{3 x} \times e^c=A e^{3 x}\) Show Worked Solution \(\dfrac{d y}{d x}\) \(=3 y\) \(\displaystyle \int \frac{1}{y}\, d y\) \(=\displaystyle \int 3\, d x\) \(\ln \abs{y}\) \(=3 x+c\) \(\abs{y}\) \(=e^{3 x+c}\) \(y\) \(=e^{3 x} \times e^c=A e^{3 x}\)