Section 1
First order and first degree differential equations
$$\frac{d y}{d x}=\frac{y+b}{x+a}$$
$$e^{x} \tan y d x+\left(1-e^{x}\right) \sec ^{2} y d y=0$$
$$x \sqrt{1+y^{2}} d x+y \sqrt{1-x^{2}} d y=0$$
$$\sqrt{1-x^{2}} \sin ^{-1} x d y+y d x=0$$
$$\frac{d y}{d x}+\sqrt{\frac{1-y^{2}}{1-x^{2}}}=0$$
$$x \sqrt{1+y^{2}} d x+y \sqrt{1+x^{2}} d y=0$$
$$y d x-x d y+3 x^{2} y^{2} e^{x^{2}} d x=0$$
$$\left(y^{2}-x^{2}\right) y^{\prime}+2 x y=0$$
$$\sqrt{1+x^{2}} \sqrt{1+y^{2}} d x+d y=0$$
$$2 x e^{x^{2}+y^{2}}=(1+2 y) e^{-y} \frac{d y}{d x}$$
$$(x-y)^{2} \frac{d y}{d x}=a^{2}$$
$$\frac{d y}{d x}=\cos (x+y)$$
$$\frac{d y}{d x}=\frac{x(2 \log x+1)}{\sin y+y \cos y}$$
$$x(x-1) \frac{d y}{d x}+y(y-1)=0$$
$$\left(x^{2}+1\right) \frac{d y}{d x}+y^{2}+1=0 \quad y(0)=1$$
$$x \frac{d y}{d x}+y+4=0$$
$$\frac{d y}{d x}=\frac{x+x^{2}}{y-y^{2}}$$
$$y-x \frac{d y}{d x}=3\left(1+x^{2} \frac{d y}{d x}\right)$$
$$\left(e^{y}+1\right) \cos x d x+e^{y} \sin x d y=0$$
$$y^{2} \cos \sqrt{x}-2 \sqrt{x} e^{1 / y} d y=0$$
$$3 e^{x} \cos ^{2} y d x+\left(1+e^{x}\right) \cot y d y=0$$
$$\cos (x+y) d y=d x$$
$$\frac{d y}{d x}+1=e^{x+y}$$
$$\left(\frac{x+y-a}{x+y-b}\right) \frac{d y}{d x}=\left(\frac{x+y+a}{x+y+b}\right)$$