5.3.22 Problems 2101 to 2200

Table 5.89: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

8709

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

8715

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

8719

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

8720

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

8732

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

8734

\[ {} 2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0 \]

8736

\[ {} y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7} \]

8738

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

8745

\[ {} y^{\prime } = \frac {3 x -y+1}{2 x +y+4} \]

8751

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

8753

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

8754

\[ {} \frac {2 y y^{\prime } x}{3} = \sqrt {x^{6}-y^{4}}+y^{2} \]

8760

\[ {} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime } = 0 \]

8763

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

8766

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

8767

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

8769

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

8770

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

8771

\[ {} y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0 \]

8772

\[ {} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0 \]

8775

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

8776

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

8777

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

8779

\[ {} -y+x y^{\prime }+x^{3} y^{\prime \prime } = \cos \left (\frac {1}{x}\right ) \]

8780

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

8781

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

8782

\[ {} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y = x +\frac {1}{x} \]

8783

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

8784

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

8785

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2} \]

8786

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

8787

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

8793

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

8794

\[ {} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0 \]

8799

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

8800

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

8809

\[ {} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \]

8811

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

8813

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

8814

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

8819

\[ {} x x^{\prime \prime }-{x^{\prime }}^{2} = 0 \]

8821

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

8828

\[ {} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0 \]

8832

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

8834

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

8835

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

8838

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

8839

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

8842

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

8843

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

8844

\[ {} \left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z = 0 \]

8845

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

8849

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

8851

\[ {} y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2} = 0 \]

8962

\[ {} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0 \]

8965

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

8966

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

8967

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

8968

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

8981

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

8983

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

8984

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

8996

\[ {} x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y = 0 \]

9000

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

9003

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

9006

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

9021

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

9023

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

9033

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

9039

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

9043

\[ {} 5 y^{2} x^{3}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime } = 0 \]

9047

\[ {} y y^{\prime \prime }+4 {y^{\prime }}^{2} = 0 \]

9049

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

9053

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

9054

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

9058

\[ {} [y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+x y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right ) x -y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right )] \]

9065

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

9130

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

9135

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

9137

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

9138

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

9139

\[ {} 2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime } \]

9142

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

9145

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

9147

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

9151

\[ {} {\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0 \]

9155

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

9164

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

9170

\[ {} y^{\prime } = \frac {x +y-1}{x +4 y+2} \]

9177

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

9179

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

9180

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

9184

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

9187

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

9188

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

9191

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

9192

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

9195

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

9196

\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \]

9199

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