Question

3. Find the general solution of the differential equation : \( \frac{d y}{d x}=\frac{3 e^{2 x}+3 e^{4 x}}{e^{x}+e^{-x}} \)

Answer 1

\(\frac{dy}{dx}=\frac{3e^{2x}+3e^{4x}}{e^x+e^{-x}}\) = \(\frac{3e^{2x}(1+e^{2x})e^x}{e^{2x}+1}\)

 = 3e^3x

⇒ dy = 3e^3xdx

⇒ y = \(\frac{3e^{3x}}3+c\)

⇒ y = e^3x + c is general solution of the given differential equation.