3.1.59 Problems 5801 to 5900

Table 3.117: First order ode

#

ODE

Mathematica

Maple

12726

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

12727

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

12728

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

12729

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

12730

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

12731

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

12732

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

12733

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

12734

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

12735

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

12736

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

12737

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

12738

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

12739

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

12740

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

12741

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

12742

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

12743

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

12773

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

12785

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

12787

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

12792

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

12793

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

12799

\[ {}y^{\prime }-2 y = 6 \]

12800

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

12807

\[ {}y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

12814

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

12815

\[ {}y^{\prime }-3 y = \delta \left (-1+x \right )+2 \operatorname {Heaviside}\left (-2+x \right ) \]

12865

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

12866

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

12867

\[ {}y^{\prime } = t^{4} y \]

12868

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

12869

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

12870

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

12871

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

12872

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

12873

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

12874

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

12875

\[ {}y^{\prime } = t y^{\frac {1}{3}} \]

12876

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

12877

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

12878

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

12879

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

12880

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

12881

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

12882

\[ {}y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}} \]

12883

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

12884

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

12885

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

12886

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

12887

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

12888

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

12889

\[ {}y^{\prime } = t^{2} y^{3} \]

12890

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

12891

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

12892

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

12893

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

12894

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

12895

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

12896

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

12897

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

12898

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

12899

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

12900

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

12901

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

12902

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

12903

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

12904

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

12905

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

12906

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

12907

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

12908

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

12909

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

12910

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

12911

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

12912

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

12913

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

12914

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

12915

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

12916

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

12917

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

12918

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

12919

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

12920

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

12921

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

12922

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

12923

\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]

12924

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

12925

\[ {}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \]

12926

\[ {}v^{\prime } = -\frac {v}{R C} \]

12927

\[ {}v^{\prime } = \frac {K -v}{R C} \]

12928

\[ {}v^{\prime } = 2 V \left (t \right )-2 v \]

12929

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

12930

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

12931

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

12932

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

12933

\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \]

12934

\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \]

12935

\[ {}y^{\prime } = {\mathrm e}^{\frac {2}{y}} \]

12936

\[ {}y^{\prime } = {\mathrm e}^{\frac {2}{y}} \]