3.9.50 Problems 4901 to 5000

Table 3.605: First order ode linear in derivative




#

ODE

Mathematica

Maple





12701

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





12702

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





12703

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





12704

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





12705

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





12706

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





12707

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





12708

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





12709

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





12710

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





12711

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





12712

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





12713

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





12714

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





12715

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





12716

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





12717

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





12718

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





12719

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





12720

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





12721

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





12722

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





12723

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





12724

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





12725

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





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

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