The process of solving exact differential equations entails ascertaining the exactness of a given equation, followed by the utilization of the properties intrinsic to exact differentials to pinpoint a potential function. This identified function serves as the solution to the equation in question. The techniques employed typically encompass integration and the identification of patterns within the differential constituents.
| Topic | Problem | Solution |
|---|---|---|
| None | Find $\frac{d y}{d x}$ \[ e^{4 x}=\sin (x+2 y) \] | Differentiate both sides of the equation with respect to x. The derivative of \(e^{4x}\) with respe… |