6.199 Problems 19801 to 19900

Table 6.397: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

19801

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

19802

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

19803

\[ {} x^{\prime \prime }-5 x^{\prime }+6 x = 0 \]

19804

\[ {} x^{\prime \prime }-4 x^{\prime }+4 x = 0 \]

19805

\[ {} x^{\prime \prime }-4 x^{\prime }+5 x = 0 \]

19806

\[ {} x^{\prime \prime }+3 x^{\prime } = 0 \]

19807

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

19808

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

19809

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

19810

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

19811

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

19812

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

19813

\[ {} x^{\prime \prime }+2 x^{\prime }+4 x = {\mathrm e}^{t} \cos \left (2 t \right ) \]

19814

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

19815

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

19816

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

19817

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

19818

\[ {} y^{\prime }+c y = a \]

19819

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

19820

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

19821

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

19822

\[ {} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]

19823

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

19824

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

19825

\[ {} v^{\prime }+\frac {2 v}{u} = 3 \]

19826

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

19827

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

19828

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

19829

\[ {} x^{\prime } = k \left (A -n x\right ) \left (M -m x\right ) \]

19830

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

19831

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

19832

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

19833

\[ {} 2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g \]

19834

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

19835

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

19836

\[ {} \frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0 \]

19837

\[ {} \left (T+\frac {1}{\sqrt {t^{2}-T^{2}}}\right ) T^{\prime } = \frac {T}{t \sqrt {t^{2}-T^{2}}}-t \]

19838

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

19839

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

19840

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

19841

\[ {} p^{\prime } = \frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \]

19842

\[ {} \left (T \ln \left (t \right )-1\right ) T = t T^{\prime } \]

19843

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

19844

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

19845

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

19846

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

19847

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

19848

\[ {} \sqrt {t^{2}+T} = T^{\prime } \]

19849

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

19850

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

19851

\[ {} \theta ^{\prime \prime } = -p^{2} \theta \]

19852

\[ {} \sec \left (\theta \right )^{2} = \frac {m s^{\prime }}{k} \]

19853

\[ {} y^{\prime \prime } = \frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \]

19854

\[ {} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]

19855

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

19856

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

19857

\[ {} v^{\prime }+\frac {2 v}{u} = 3 v \]

19858

\[ {} \sqrt {-u^{2}+1}\, v^{\prime } = 2 u \sqrt {1-v^{2}} \]

19859

\[ {} \sqrt {1+v^{\prime }} = \frac {{\mathrm e}^{u}}{2} \]

19860

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

19861

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

19862

\[ {} v^{\prime }+2 u v = 2 u \]

19863

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

19864

\[ {} u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2} = 1 \]

19865

\[ {} 4 {y^{\prime }}^{3} y-2 x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x +x^{3} = 16 y^{2} \]

19866

\[ {} \theta ^{\prime \prime }-p^{2} \theta = 0 \]

19867

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

19868

\[ {} y^{\prime \prime }+12 y = 7 y^{\prime } \]

19869

\[ {} r^{\prime \prime }-a^{2} r = 0 \]

19870

\[ {} y^{\prime \prime \prime \prime }-a^{4} y = 0 \]

19871

\[ {} v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u} \]

19872

\[ {} y^{\prime \prime }+4 y^{\prime }-y = \sin \left (t \right ) \]

19873

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

19874

\[ {} 5 x^{\prime }+x = \sin \left (3 t \right ) \]

19875

\[ {} x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime } = {\mathrm e}^{-3 t} \]

19876

\[ {} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime } = 17 x^{6} \]

19877

\[ {} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x = \cos \left (3 \ln \left (t \right )\right ) \]

19878

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

19879

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

19880

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

19881

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

19882

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

19883

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

19884

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

19885

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

19886

\[ {} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0 \]

19887

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

19888

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

19889

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

19890

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

19891

\[ {} y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0 \]

19892

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x} \]

19893

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x} \]

19894

\[ {} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

19895

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

19896

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

19897

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

19898

\[ {} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0 \]

19899

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

19900

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