4.9.82 Problems 8101 to 8200

Table 4.1001: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

22687

\[ {} x y^{\prime }-y = 2 x^{2} y^{2} y^{\prime } \]

22688

\[ {} x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )+y \]

22689

\[ {} y^{\prime } = 2-\frac {y}{x} \]

22691

\[ {} i^{\prime } = \frac {i t^{2}}{t^{3}-i^{3}} \]

22692

\[ {} \left ({\mathrm e}^{y}+x +3\right ) y^{\prime } = 1 \]

22693

\[ {} r^{\prime } = {\mathrm e}^{t}-3 r \]

22696

\[ {} y^{\prime } = \frac {3 y+x}{x -3 y} \]

22697

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

22698

\[ {} {\mathrm e}^{2 x -y}+{\mathrm e}^{y-2 x} y^{\prime } = 0 \]

22699

\[ {} r^{3} r^{\prime } = \sqrt {a^{8}-r^{8}} \]

22700

\[ {} 2 x^{2}-y \,{\mathrm e}^{x}-{\mathrm e}^{x} y^{\prime } = 0 \]

22701

\[ {} x y^{\prime }+2 y-x \cos \left (x \right ) = 0 \]

22702

\[ {} y^{\prime } \sqrt {x^{3}+1} = x^{2} y+x^{2} \]

22703

\[ {} 3 y^{2}+4 x y+\left (x^{2}+2 x y\right ) y^{\prime } = 0 \]

22704

\[ {} y^{\prime } = y \left (x +y\right ) \]

22705

\[ {} y^{\prime } = x \left (x +y\right ) \]

22707

\[ {} y^{\prime } = 1-\left (x -y\right )^{2} \]

22708

\[ {} y^{\prime } = \frac {{\mathrm e}^{x -y}}{y} \]

22709

\[ {} y^{2}+y y^{\prime } x = \sin \left (x \right ) \]

22710

\[ {} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0 \]

22711

\[ {} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]

22712

\[ {} y^{\prime } = \frac {2}{x +2 y-3} \]

22713

\[ {} y^{\prime } = \sqrt {\sin \left (x \right )+y}-\cos \left (x \right ) \]

22714

\[ {} y^{\prime } = \tan \left (x +y\right ) \]

22715

\[ {} y^{\prime } = {\mathrm e}^{3 y+x}+1 \]

22717

\[ {} x^{2} y^{3}+2 x y^{2}+y+\left (y^{2} x^{3}-2 x^{2} y+x \right ) y^{\prime } = 0 \]

22719

\[ {} y^{\prime } = \frac {x +y^{2}}{2 y} \]

22720

\[ {} y^{\prime } = \sqrt {y}+x \]

22721

\[ {} y^{\prime } = \sqrt {\frac {5 x -6 y}{5 x +6 y}} \]

22722

\[ {} y^{\prime }+x y = x^{2}+1 \]

22723

\[ {} x^{2} y+2 y^{4}+\left (x^{3}+3 x y^{3}\right ) y^{\prime } = 0 \]

22724

\[ {} y^{\prime } = \frac {y}{x} \]

22725

\[ {} x^{2}+y^{2}+2 y y^{\prime } x = 0 \]

22726

\[ {} y^{\prime } = x y^{2}-2 y+4-4 x \]

22727

\[ {} y^{\prime }+y^{2} = x^{2}+1 \]

22728

\[ {} y^{\prime } = \frac {y^{2}}{x -1}-\frac {x y}{x -1}+1 \]

22920

\[ {} x y^{\prime } = x^{2} y^{2}-y+1 \]

22934

\[ {} y^{\prime }+2 y = 5 \delta \left (t -1\right ) \]

23063

\[ {} y y^{\prime } = x^{2} \]

23064

\[ {} y^{\prime } \left (1+x \right ) = 1+y \]

23065

\[ {} 1+y^{2} = \left (x^{2}+1\right ) y^{\prime } \]

23066

\[ {} y^{\prime } \sin \left (y\right ) = \sec \left (x \right )^{2} \]

23067

\[ {} x^{\prime } = \frac {x}{t} \]

23068

\[ {} y^{\prime } \left (-x^{2}+1\right ) = 1-y^{2} \]

23069

\[ {} \frac {\tan \left (y\right )}{\cos \left (x \right )} = \cos \left (x \right ) y^{\prime } \]

23070

\[ {} x y^{\prime } = \left (1+x \right ) y^{2} \]

23071

\[ {} x \cos \left (y\right ) y^{\prime }-\left (x^{2}+1\right ) \sin \left (y\right ) = 0 \]

23072

\[ {} \left (x^{2}-1\right ) y^{\prime } = x \left (y-1\right ) \]

23073

\[ {} x \left (y+2\right )+y \left (x +2\right ) y^{\prime } = 0 \]

23074

\[ {} x y \left (x^{2}+1\right ) y^{\prime }-y^{2} = 1 \]

23075

\[ {} x y^{\prime }+y = 0 \]

23076

\[ {} x y^{\prime }+y-1 = 0 \]

23077

\[ {} y-x y^{\prime } = 3 y^{2} y^{\prime } \]

23078

\[ {} 2 x y+x^{2} y^{\prime } = 0 \]

23079

\[ {} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 5 \]

23080

\[ {} y^{\prime } = \frac {\sin \left (x \right ) \sin \left (y\right )}{\cos \left (x \right ) \cos \left (y\right )} \]

23081

\[ {} x \sec \left (y\right )^{2} y^{\prime }+1+\tan \left (y\right ) = 0 \]

23082

\[ {} {\mathrm e}^{y} \left (x y^{\prime }+1\right ) = 5 \]

23083

\[ {} {\mathrm e}^{x} \left (y^{\prime }+y\right ) = 3 \]

23084

\[ {} \frac {y}{x}+\ln \left (x \right ) y^{\prime } = 2 \]

23085

\[ {} y^{\prime } = \frac {x -y}{x +y} \]

23086

\[ {} y^{\prime } = 1+\frac {y}{x} \]

23087

\[ {} y^{\prime } = \frac {x^{2}+y^{2}}{x y} \]

23088

\[ {} y^{\prime } = \frac {y}{x}-\frac {x}{y} \]

23089

\[ {} y^{\prime } = \frac {x -y+1}{x +y+1} \]

23090

\[ {} y^{\prime } = \frac {x -y+2}{1+x} \]

23091

\[ {} y^{\prime } = \frac {x +y+2}{1+x} \]

23092

\[ {} y^{\prime }+3 y = 5 \]

23093

\[ {} y^{\prime }+2 x y = x \]

23094

\[ {} y^{\prime }-2 x y = 3 x \]

23095

\[ {} y^{\prime }+7 y = {\mathrm e}^{5 x} \]

23096

\[ {} y^{\prime }-6 y = {\mathrm e}^{6 t} \]

23097

\[ {} y^{\prime }-6 y = {\mathrm e}^{6 t} \]

23098

\[ {} z^{\prime }-z \sin \left (x \right ) = {\mathrm e}^{-\cos \left (x \right )} \]

23099

\[ {} z^{\prime }-z \sin \left (x \right ) = {\mathrm e}^{-\cos \left (x \right )} \]

23100

\[ {} y^{\prime }-\frac {3 y}{x} = 5 x \]

23101

\[ {} y^{\prime }-\frac {6 y}{x} = 7 x \]

23102

\[ {} y^{\prime }-\sin \left (x \right ) y = \sin \left (x \right ) \]

23103

\[ {} y^{\prime }+y \tan \left (x \right ) = \sec \left (x \right ) \]

23104

\[ {} \left ({\mathrm e}^{x}+1\right ) y^{\prime }+y \,{\mathrm e}^{x} = {\mathrm e}^{x} \]

23105

\[ {} \left (x^{2}+1\right ) y^{\prime }+x y = \left (x^{2}+1\right )^{{3}/{2}} \]

23106

\[ {} p^{\prime } = 15-20 p \]

23107

\[ {} n^{\prime } = k n-b t \]

23108

\[ {} x y^{\prime }-2 y \cos \left (x \right ) = {\mathrm e}^{x} \sin \left (x \right )^{3} \]

23109

\[ {} y^{\prime } \sin \left (x \right )+2 y \cos \left (x \right ) = 4 \cos \left (x \right )^{3} \]

23110

\[ {} y^{\prime } = \frac {x y+a^{2}}{a^{2}-x^{2}} \]

23111

\[ {} y^{\prime }+\frac {y \ln \left (x \right )}{x} = 2 \]

23112

\[ {} y^{\prime }+4 y = {\mathrm e}^{k x} \]

23113

\[ {} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y = x \]

23114

\[ {} v^{\prime } = 60 t -4 v \]

23171

\[ {} r^{\prime } = -a \sin \left (\theta \right ) \]

23172

\[ {} \frac {r^{\prime }}{r} = \tan \left (\theta \right ) \]

23173

\[ {} \left (1+\cos \left (\theta \right )\right ) r^{\prime } = -r \sin \left (\theta \right ) \]

23174

\[ {} \cot \left (\theta \right ) r^{\prime } = r+b \]

23175

\[ {} r r^{\prime } = a \]

23176

\[ {} r^{\prime } \left (1+\frac {\cos \left (\theta \right )}{2}\right )-r \sin \left (\theta \right ) = 0 \]

23177

\[ {} \sin \left (\theta \right )^{2} r^{\prime } = -b \cos \left (\theta \right ) \]

23178

\[ {} r^{\prime } = 0 \]

23179

\[ {} r^{\prime } = c \]

23180

\[ {} r^{\prime } \left (\sin \left (\theta \right )-m \cos \left (\theta \right )\right )+r \left (\cos \left (\theta \right )+m \sin \left (\theta \right )\right ) = 0 \]