Chapter 1 - First-Order Differential Equations - 1.9 Exact Differential Equations - True-False Review - Page 91: f

True

$(2ye^{2x}-\sin y)dx+(e^{2x}-x\cos y)dy=0$ Here, $M(x,y)=2ye^{2x}-\sin y$ $N(x,y)=e^{2x}-x\cos y$ $M_y=2e^{2x}-\cos y\;\;\;, \;\;\;N_x=2e^{2x}-\cos y$ $\Rightarrow M_y=N_x$ That's why (1) ia exact differential equation.