$$y^{\prime }=y^2-{\lambda }^2+\frac{f(\coth \left(\lambda x\right))}{\sinh {\left(\lambda x\right)}^4}$$

$$y^{\prime }=y^2-{\lambda }^2+\frac{f(\tanh \left(\lambda x\right))}{\cosh {\left(\lambda x\right)}^4}$$

$$x^2{y}^{\prime }=x^2{y}^2+f(a\ln (x)+b)+\frac{1}{4}$$

$$y^{\prime }=y^2+{\lambda }^2+\frac{f(\cot \left(\lambda x\right))}{\sin {\left(\lambda x\right)}^4}$$

$$y^{\prime }=y^2+{\lambda }^2+\frac{f(\tan \left(\lambda x\right))}{\cos {\left(\lambda x\right)}^4}$$

$$y^{\prime }=y^2+{\lambda }^2+\frac{f\left(\frac{\sin (\lambda x+a)}{\sin (\lambda x+b)}\right)}{\sin {(\lambda x+b)}^4}$$

$$y{y}^{\prime }-y=A$$

$$y{y}^{\prime }-y=Ax+B$$

$$y{y}^{\prime }-y=-\frac{2x}{9}+A+\frac{B}{\sqrt{x}}$$

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

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

$$y{y}^{\prime }-y=A{x}^{k-1}-kB{x}^k+k{B}^2{x}^{2k-1}$$

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

$$y{y}^{\prime }-y=A+B{\mathrm{e}}^{-\frac{2x}{A}}$$

$$y{y}^{\prime }-y=A({\mathrm{e}}^{\frac{2x}{A}}-1)$$

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

$$y{y}^{\prime }-y=-\frac{2x}{9}+6A^2(1+\frac{2A}{\sqrt{x}})$$

$$y{y}^{\prime }-y=\frac{2m-2}{{(m-3)}^2}+\frac{2A(m(m+3)\sqrt{x}+(4m^2+3m+9)A+\frac{3m(m+3)A^2}{\sqrt{x}})}{{(m-3)}^2}$$

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

$$y{y}^{\prime }-y=\frac{4}{9}x+2A{x}^2+2A^2{x}^3$$

$$y{y}^{\prime }-y=-\frac{3x}{16}+\frac{5A}{x^{\frac{1}{3}}}-\frac{12A^2}{x^{\frac{5}{3}}}$$

$$y{y}^{\prime }-y=\frac{A}{x}$$

$$y{y}^{\prime }-y=-\frac{x}{4}+\frac{A(\sqrt{x}+5A+\frac{3A^2}{\sqrt{x}})}{4}$$

$$y{y}^{\prime }-y=\frac{2a^2}{\sqrt{8a^2+x^2}}$$

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

$$y{y}^{\prime }-y=-\frac{6X}{25}+\frac{2A(2\sqrt{x}+19A+\frac{6A^2}{\sqrt{x}})}{25}$$

$$y{y}^{\prime }-y=\frac{3x}{8}+\frac{3\sqrt{a^2+x^2}}{8}-\frac{a^2}{16\sqrt{a^2+x^2}}$$

$$y{y}^{\prime }-y=-\frac{4x}{25}+\frac{A}{\sqrt{x}}$$

$$y{y}^{\prime }-y=-\frac{9x}{100}+\frac{A}{x^{\frac{5}{3}}}$$

$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{2A(5\sqrt{x}+34A+\frac{15A^2}{\sqrt{x}})}{49}$$

$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{A(25\sqrt{x}+41A+\frac{10A^2}{\sqrt{x}})}{98}$$

$$y{y}^{\prime }-y=-\frac{2x}{9}+\frac{A}{\sqrt{x}}$$

$$y{y}^{\prime }-y=-\frac{5x}{36}+\frac{A}{x^{\frac{7}{5}}}$$

$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{6A(-3\sqrt{x}+23A+\frac{12A^2}{\sqrt{x}})}{49}$$

$$y{y}^{\prime }-y=-\frac{30x}{121}+\frac{3A(21\sqrt{x}+35A+\frac{6A^2}{\sqrt{x}})}{242}$$

$$y{y}^{\prime }-y=-\frac{3x}{16}+\frac{A}{x^{\frac{5}{3}}}$$

$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{4A(-10\sqrt{x}+27A+\frac{10A^2}{\sqrt{x}})}{49}$$

$$y{y}^{\prime }-y=\frac{A}{\sqrt{x}}$$

$$y{y}^{\prime }-y=\frac{A}{x^2}$$

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

$$y{y}^{\prime }-y=A(n+2)(\sqrt{x}+2(n+2)A+\frac{(2n+3)A^2}{\sqrt{x}})$$

$$y{y}^{\prime }-y=A\sqrt{x}+2A^2+\frac{B}{\sqrt{x}}$$

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

$$y{y}^{\prime }-y=-\frac{x}{4}+\frac{6A(\sqrt{x}+8A+\frac{5A^2}{\sqrt{x}})}{49}$$

$$y{y}^{\prime }-y=-\frac{6x}{25}+\frac{6A(2\sqrt{x}+7A+\frac{4A^2}{\sqrt{x}})}{25}$$

$$y{y}^{\prime }-y=-\frac{3x}{16}+\frac{3A}{x^{\frac{1}{3}}}-\frac{12A^2}{x^{\frac{5}{3}}}$$

$$y{y}^{\prime }-y=\frac{3x}{8}+\frac{3\sqrt{b^2+x^2}}{8}+\frac{3b^2}{16\sqrt{b^2+x^2}}$$

$$y{y}^{\prime }-y=\frac{9x}{32}+\frac{15\sqrt{b^2+x^2}}{32}+\frac{3b^2}{64\sqrt{b^2+x^2}}$$

$$y{y}^{\prime }-y=-\frac{3x}{32}-\frac{3\sqrt{a^2+x^2}}{32}+\frac{15a^2}{64\sqrt{a^2+x^2}}$$

$$y{y}^{\prime }-y=A{x}^2-\frac{9}{625A}$$

$$y{y}^{\prime }-y=-\frac{6}{25}x-A{x}^2$$

$$y{y}^{\prime }-y=\frac{6}{25}x-A{x}^2$$

$$y{y}^{\prime }-y=12x+\frac{A}{x^{\frac{5}{2}}}$$

$$y{y}^{\prime }-y=\frac{63x}{4}+\frac{A}{x^{\frac{5}{3}}}$$

$$y{y}^{\prime }-y=2x+2A(10\sqrt{x}+31A+\frac{30A^2}{\sqrt{x}})$$

$$y{y}^{\prime }-y=2x+2A(-10\sqrt{x}+19A+\frac{30A^2}{\sqrt{x}})$$

$$y{y}^{\prime }-y=-\frac{28x}{121}+\frac{2A(5\sqrt{x}+106A+\frac{65A^2}{\sqrt{x}})}{121}$$

$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{A(5\sqrt{x}+262A+\frac{65A^2}{\sqrt{x}})}{49}$$

$$y{y}^{\prime }-y=-\frac{12x}{49}+A\sqrt{x}$$

$$y{y}^{\prime }-y=6x+\frac{A}{x^4}$$

$$y{y}^{\prime }-y=20x+\frac{A}{\sqrt{x}}$$

$$y{y}^{\prime }-y=\frac{15x}{4}+\frac{A}{x^7}$$

$$y{y}^{\prime }-y=-\frac{10x}{49}+\frac{2A(4\sqrt{x}+61A+\frac{12A^2}{\sqrt{x}})}{49}$$

$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{2A(\sqrt{x}+166A+\frac{55A^2}{\sqrt{x}})}{49}$$

$$y{y}^{\prime }-y=-\frac{4x}{25}+\frac{A(7\sqrt{x}+49A+\frac{6A^2}{\sqrt{x}})}{50}$$

$$y{y}^{\prime }-y=\frac{15x}{4}+\frac{6A}{x^{\frac{1}{3}}}-\frac{3A^2}{x^{\frac{5}{3}}}$$

$$y{y}^{\prime }-y=-\frac{3x}{16}+\frac{A}{x^{\frac{1}{3}}}+\frac{B}{x^{\frac{5}{3}}}$$

$$y{y}^{\prime }-y=-\frac{5x}{36}+\frac{A}{x^{\frac{3}{5}}}-\frac{B}{x^{\frac{7}{5}}}$$

$$y{y}^{\prime }-y=\frac{k}{\sqrt{A{x}^2+Bx+c}}$$

$$y{y}^{\prime }-y=-\frac{12x}{49}+3A(\frac{1}{49}+B)\sqrt{x}+3A^2(\frac{4}{49}-\frac{5B}{2})+\frac{15A^3(\frac{1}{49}-\frac{5B}{4})}{4\sqrt{x}}$$

$$y{y}^{\prime }-y=-\frac{6x}{25}+\frac{4B^2((-A+2)x^{\frac{1}{3}}-\frac{3B(2A+1)}{2}+\frac{B^2(1-3A)}{x^{\frac{1}{3}}}-\frac{A{B}^3}{x^{\frac{2}{3}}})}{75}$$

$$y{y}^{\prime }-y=\frac{3x}{4}-\frac{3A{x}^{\frac{1}{3}}}{2}+\frac{3A^2}{4x^{\frac{1}{3}}}-\frac{27A^4}{625x^{\frac{5}{3}}}$$

$$y{y}^{\prime }-y=-\frac{6x}{25}+\frac{7A{x}^{\frac{1}{3}}}{5}+\frac{31A^2}{3x^{\frac{1}{3}}}-\frac{100A^4}{3x^{\frac{5}{3}}}$$

$$y{y}^{\prime }-y=-\frac{10x}{49}+\frac{13A^2}{5x^{\frac{1}{5}}}-\frac{7A^3}{20x^{\frac{4}{5}}}$$

$$y{y}^{\prime }-y=-\frac{33x}{169}+\frac{286A^2}{3x^{\frac{5}{11}}}-\frac{770A^3}{9x^{\frac{13}{11}}}$$

$$y{y}^{\prime }-y=-\frac{21x}{100}+\frac{7A^2(\frac{123}{x^{\frac{1}{7}}}+\frac{280A}{x^{\frac{5}{7}}}-\frac{400A^2}{x^{\frac{9}{7}}})}{9}$$

$$y{y}^{\prime }-y=ax+b{x}^m$$

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

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

$$y{y}^{\prime }-y=a^2\lambda {\mathrm{e}}^{2\lambda x}+a\lambda x{\mathrm{e}}^{\lambda x}+b{\mathrm{e}}^{\lambda x}$$

$$y{y}^{\prime }-y=2a^2\lambda \sin \left(2\lambda x\right)+2a\sin \left(\lambda x\right)$$

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

$$y{y}^{\prime }=(ax+b)y+1$$

$$y{y}^{\prime }=\frac{y}{{(ax+b)}^2}+1$$

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

$$y{y}^{\prime }=\frac{y}{\sqrt{ax+b}}+1$$

$$y{y}^{\prime }=\frac{3y}{\sqrt{a{x}^{\frac{3}{2}}+8x}}+1$$

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

$$y{y}^{\prime }=a{\mathrm{e}}^{\lambda x}y+1$$

$$y{y}^{\prime }=({\mathrm{e}}^{\lambda x}a+b{\mathrm{e}}^{-\lambda x})y+1$$

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

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

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

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

$$y{y}^{\prime }=(ax+3b)y+c{x}^3-ab{x}^2-2b^{2}x$$

$$y{y}^{\prime }=(3ax+b)y-a^2{x}^3-ab{x}^2+cx$$

$$2y{y}^{\prime }=(7ax+5b)y-3a^2{x}^3-2c{x}^2-3b^{2}x$$

$$y{y}^{\prime }=((3-m)x-1)y-(m-1)ax$$

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

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