Separation of variables: general and particular solutions Problem set A Answers

1. (a) \(y=Ae^{5x}\)
2. (b) \(y=6+Ae^{0.2x}\)
3. (c) \(y=4-Ae^{-x}\)

1. (a) \(y=-\dfrac{1}{2x^2+A}\)
2. (b) \(y=Ax^3\)
3. (c) \(y=\sqrt{\dfrac{10x^3}{3}+A}\)

1. (a) \(y=\ln(A-\cos x)\)
2. (b) \(y=Ae^{e^{2x}/2}\)

1. (a) \(y=2e^{3x^2/2}\)
2. (b) \(y=\sqrt[3]{6x^2+21}\)

Shown: \(y=1+3e^{x^2/2}\)

Shown: \(\tan y=x^3+c\)

\(y=\dfrac{2x}{x+2}\)