Chapter D1.3, Problem 35E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

1. a. The equation $u^{\prime }\left(x\right)={\left(x^2{u}^7\right)}^{-1}$ is separable.
2. b. The general solution of the separable equation $y^{\prime }\left(t\right)=\frac{t}{y^7+10y^4}$ can be expressed explicitly with y in terms of t.
3. c. The general solution of the equation $y{y}^{\prime }\left(x\right)=x{e}^{-y}$ can be found using integration by parts.