6.188 Problems 18701 to 18800

Table 6.375: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

18701

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

18702

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

18703

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

18704

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

18705

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

18706

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

18707

\[ {} \left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2} \]

18708

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

18709

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

18710

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

18711

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

18712

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

18713

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

18714

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

18715

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

18716

\[ {} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0 \]

18717

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

18718

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

18719

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

18720

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

18721

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

18722

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

18723

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

18724

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

18725

\[ {} {y^{\prime }}^{3} = a \,x^{4} \]

18726

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

18727

\[ {} {y^{\prime }}^{2}-7 y^{\prime }+12 = 0 \]

18728

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

18729

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

18730

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

18731

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

18732

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

18733

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

18734

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

18735

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

18736

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

18737

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

18738

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

18739

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

18740

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

18741

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

18742

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

18743

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

18744

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

18745

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

18746

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

18747

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

18748

\[ {} {y^{\prime }}^{2}-9 y^{\prime }+18 = 0 \]

18749

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

18750

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

18751

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

18752

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

18753

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

18754

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

18755

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

18756

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

18757

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

18758

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

18759

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

18760

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

18761

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

18762

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

18763

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

18764

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

18765

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

18766

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

18767

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

18768

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

18769

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

18770

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

18771

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

18772

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

18773

\[ {} \left (1+y^{\prime }\right )^{3} = \frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a} \]

18774

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

18775

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

18776

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

18777

\[ {} a {y^{\prime }}^{3} = 27 y \]

18778

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

18779

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

18780

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

18781

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

18782

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

18783

\[ {} 4 {y^{\prime }}^{2} = 9 x \]

18784

\[ {} 4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0 \]

18785

\[ {} \left (8 {y^{\prime }}^{3}-27\right ) x = 12 y {y^{\prime }}^{2} \]

18786

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

18787

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

18788

\[ {} y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

18789

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

18790

\[ {} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

18791

\[ {} 9 y^{\prime \prime }+18 y^{\prime }-16 y = 0 \]

18792

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

18793

\[ {} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

18794

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

18795

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

18796

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

18797

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

18798

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

18799

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

18800

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y = X \left (x \right ) \]