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

1. (a) \(y=Ae^{-3x}\)
2. (b) \(y=5+Ae^{0.4x}\)
3. (c) \(y=9-Ae^{-2x}\)

1. (a) \(y=-\dfrac{1}{3x^2+A}\)
2. (b) \(y=Ax^5\)
3. (c) \(y=\sqrt{\dfrac{14x^3}{3}+A}\)

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

1. (a) \(y=3e^{5x^2/2}\)
2. (b) \(y=\sqrt[3]{9x^2-1}\)

Shown: \(y=4e^{x^2}-1\)

Shown: \(\tan y=e^{x}+c\)

\(y=\dfrac{x}{x+1}\)