$$(-x^2+1)y^{\prime }=a+4xy$$

$$(x^2+1)y^{\prime }=(2bx+a)y$$

$$(x^2+1)y^{\prime }=1+y^2$$

$$(-x^2+1)y^{\prime }=1-y^2$$

$$(-x^2+1)y^{\prime }=1-(2x-y)y$$

$$(-x^2+1)y^{\prime }=n(1-2xy+y^2)$$

$$(x^2+1)y^{\prime }+xy(1-y)=0$$

$$(-x^2+1)y^{\prime }=xy(1+ay)$$

$$(x^2+1)y^{\prime }=1+y^2-2xy(1+y^2)$$

$$(x^2+1)y^{\prime }+x\sin \left(y\right)\cos \left(y\right)=x(x^2+1)\cos {\left(y\right)}^2$$

$$(x^2+1)y^{\prime }=1+x^2-y\mathrm{arccot}\left(x\right)$$

$$(-x^2+4)y^{\prime }+4y=(2+x)y^2$$

$$(a^2+x^2)y^{\prime }=b+xy$$

$$(a^2+x^2)y^{\prime }=(b+y)(x+\sqrt{a^2+x^2})$$

$$(a^2+x^2)y^{\prime }+(x-y)y=0$$

$$(a^2+x^2)y^{\prime }=a^2+3xy-2y^2$$

$$(a^2+x^2)y^{\prime }+xy+bx{y}^2=0$$

$$x(1-x)y^{\prime }=a+(1+x)y$$

$$x(1-x)y^{\prime }=2+2xy$$

$$x(1-x)y^{\prime }=2xy-2$$

$$x(1+x)y^{\prime }=(-2x+1)y$$

$$x(1-x)y^{\prime }+(2x+1)y=a$$

$$x(1-x)y^{\prime }=a+2(2-x)y$$

$$x(1-x)y^{\prime }+2-3xy+y=0$$

$$x(1+x)y^{\prime }=(1+x)(x^2-1)+(x^2+x-1)y$$

$$(-2+x)(x-3)y^{\prime }+x^2-8y+3xy=0$$

$$x(x+a)y^{\prime }=(b+cy)y$$

$${(x+a)}^2{y}^{\prime }=2(x+a)(b+y)$$

$${(x-a)}^2{y}^{\prime }+k{(x+y-a)}^2+y^2=0$$

$$(x-a)(x-b)y^{\prime }+ky=0$$

$$(x-a)(x-b)y^{\prime }=(x-a)(x-b)+(2x-a-b)y$$

$$(x-a)(x-b)y^{\prime }=c{y}^2$$

$$(x-a)(x-b)y^{\prime }+k(y-a)(y-b)=0$$

$$(x-a)(x-b)y^{\prime }+k(x+y-a)(x+y-b)+y^2=0$$

$$2x^2{y}^{\prime }=y$$

$$2x^2{y}^{\prime }+x\cot \left(x\right)-1+2x^{2}y\cot \left(x\right)=0$$

$$2x^2{y}^{\prime }+1+2xy-y^2{x}^2=0$$

$$2x^2{y}^{\prime }=2xy+(1-x\cot \left(x\right))(x^2-y^2)$$

$$2(-x^2+1)y^{\prime }=\sqrt{-x^2+1}+(1+x)y$$

$$x(-2x+1)y^{\prime }+1+(1-4x)y=0$$

$$x(-2x+1)y^{\prime }=4x-(1+4x)y+y^2$$

$$2x(1-x)y^{\prime }+x+(-2x+1)y=0$$

$$2x(1-x)y^{\prime }+x+(1-x)y^2=0$$

$$2(x^2+x+1)y^{\prime }=1+8x^2-(2x+1)y$$

$$4(x^2+1)y^{\prime }-4xy-x^2=0$$

$$a{x}^2{y}^{\prime }=x^2+axy+b^2{y}^2$$

$$(b{x}^2+a)y^{\prime }=A+B{y}^2$$

$$(b{x}^2+a)y^{\prime }=cxy\ln \left(y\right)$$

$$x(ax+1)y^{\prime }+a-y=0$$

$${(bx+a)}^2{y}^{\prime }+c{y}^2+(bx+a)y^3=0$$

$$x^3{y}^{\prime }=a+b{x}^{2}y$$

$$x^3{y}^{\prime }=3-x^2+x^{2}y$$

$$x^3{y}^{\prime }=x^4+y^2$$

$$x^3{y}^{\prime }=y(x^2+y)$$

$$x^3{y}^{\prime }=x^2(y-1)+y^2$$

$$x^3{y}^{\prime }=(1+x)y^2$$

$$x^3{y}^{\prime }+20+x^{2}y(1-x^{2}y)=0$$

$$x^3{y}^{\prime }+3+(3-2x)x^{2}y-x^6{y}^2=0$$

$$x^3{y}^{\prime }=(2x^2+y^2)y$$

$$x^3{y}^{\prime }=\cos \left(y\right)(\cos \left(y\right)-2x^2\sin \left(y\right))$$

$$x(x^2+1)y^{\prime }=x^{2}a+y$$

$$x(-x^2+1)y^{\prime }=x^{2}a+y$$

$$x(x^2+1)y^{\prime }=a{x}^3+y$$

$$x(x^2+1)y^{\prime }=a-x^{2}y$$

$$x(x^2+1)y^{\prime }=(-x^2+1)y$$

$$x(-x^2+1)y^{\prime }=(x^2-x+1)y$$

$$x(-x^2+1)y^{\prime }=a{x}^3+(-2x^2+1)y$$

$$x(-x^2+1)y^{\prime }=x^3(-x^2+1)+(-2x^2+1)y$$

$$x(x^2+1)y^{\prime }=2-4x^{2}y$$

$$x(x^2+1)y^{\prime }=x-(5x^2+3)y$$

$$x(-x^2+1)y^{\prime }+x^2+(-x^2+1)y^2=0$$

$$x^2(1-x)y^{\prime }=(2-x)xy-y^2$$

$$2x^3{y}^{\prime }=(x^2-y^2)y$$

$$2x^3{y}^{\prime }=(3x^2+a{y}^2)y$$

$$6x^3{y}^{\prime }=4x^{2}y+(1-3x)y^4$$

$$x(c{x}^2+bx+a)y^{\prime }+x^2-(c{x}^2+bx+a)y=y^2$$

$$x^4{y}^{\prime }=(x^3+y)y$$

$$x^4{y}^{\prime }+a^2+x^4{y}^2=0$$

$$x^4{y}^{\prime }+x^{3}y+\csc \left(xy\right)=0$$

$$(-x^4+1)y^{\prime }=2x(1-y^2)$$

$$x(-x^3+1)y^{\prime }=2x-(-4x^3+1)y$$

$$x(-x^3+1)y^{\prime }=x^2+(1-2xy)y$$

$$x^2(-x^2+1)y^{\prime }=(x-3x^{3}y)y$$

$$x(-2x^3+1)y^{\prime }=2(-x^3+1)y$$

$${(c{x}^2+bx+a)}^2(y^{\prime }+y^2)+A=0$$

$$x^5{y}^{\prime }=1-3x^{4}y$$

$$x(-x^4+1)y^{\prime }=2x(x^2-y^2)+(-x^4+1)y$$

$$x^7{y}^{\prime }+5x^3{y}^2+2(x^2+1)y^3=0$$

$$x^n{y}^{\prime }=a+b{x}^{n-1}y$$

$$x^n{y}^{\prime }=x^{2n-1}-y^2$$

$$x^n{y}^{\prime }+x^{2n-2}+y^2+(1-n)x^{n-1}=0$$

$$x^n{y}^{\prime }=a^2{x}^{2n-2}+b^2{y}^2$$

$$x^n{y}^{\prime }=x^{n-1}(a{x}^{2n}+ny-b{y}^2)$$

$$x^k{y}^{\prime }=a{x}^m+b{y}^n$$

$$y^{\prime }\sqrt{x^2+1}=2x-y$$

$$y^{\prime }\sqrt{-x^2+1}=1+y^2$$

$$(x-\sqrt{x^2+1})y^{\prime }=y+\sqrt{1+y^2}$$

$$y^{\prime }\sqrt{a^2+x^2}+x+y=\sqrt{a^2+x^2}$$

$$y^{\prime }\sqrt{b^2+x^2}=\sqrt{y^2+a^2}$$

$$y^{\prime }\sqrt{b^2-x^2}=\sqrt{a^2-y^2}$$