5.3.11 Problems 1001 to 1100

Table 5.67: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

5658

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

5659

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

5660

\[ {} x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0 \]

5662

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

5664

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

5665

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

5666

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

5667

\[ {} 16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \]

5668

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

5669

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

5670

\[ {} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0 \]

5675

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

5676

\[ {} {y^{\prime }}^{4}-4 y {y^{\prime }}^{2} x^{2}+16 x y^{2} y^{\prime }-16 y^{3} = 0 \]

5679

\[ {} {y^{\prime }}^{4} x -2 {y^{\prime }}^{3} y+12 x^{3} = 0 \]

5680

\[ {} 3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0 \]

5685

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

5692

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

5693

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

5696

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

5697

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

5698

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

5699

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

5700

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

5701

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

5702

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

5703

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

5704

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

5712

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

5713

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

5714

\[ {} \ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y \]

5727

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

5749

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

5750

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

5751

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

5752

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

5753

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

5754

\[ {} \left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime } = 0 \]

5755

\[ {} a \,x^{k} y+y^{\prime \prime } = 0 \]

5756

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

5757

\[ {} \left (a +b \cos \left (2 x \right )+k \cos \left (4 x \right )\right ) y+y^{\prime \prime } = 0 \]

5758

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

5759

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

5760

\[ {} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a2} \csc \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0 \]

5761

\[ {} y^{\prime \prime } = \left (a^{2}+\left (-1+p \right ) p \csc \left (x \right )^{2}+\left (-1+q \right ) q \sec \left (x \right )^{2}\right ) y \]

5762

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

5763

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

5764

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

5765

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

5766

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

5767

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

5768

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

5769

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

5770

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

5772

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

5816

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

5817

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

5818

\[ {} \left (b +{\mathrm e}^{x} c \right ) y+a y^{\prime }+y^{\prime \prime } = 0 \]

5819

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

5820

\[ {} b \,{\mathrm e}^{k x} y+a y^{\prime }+y^{\prime \prime } = 0 \]

5821

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

5822

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

5823

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

5824

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

5825

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

5826

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

5827

\[ {} 6 y-2 x y^{\prime }+y^{\prime \prime } = 0 \]

5828

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

5829

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

5830

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

5831

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

5832

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

5833

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

5834

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

5835

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

5836

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

5837

\[ {} \left (\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime } = 0 \]

5838

\[ {} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime } = 0 \]

5839

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

5840

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

5841

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

5842

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

5843

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

5844

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

5845

\[ {} a k \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0 \]

5846

\[ {} -a \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0 \]

5847

\[ {} b \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0 \]

5848

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

5849

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

5850

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

5851

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

5852

\[ {} \left (\operatorname {a0} -\operatorname {a2} \csc \left (x \right )^{2}+4 \operatorname {a1} \sin \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]

5853

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

5854

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

5855

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

5856

\[ {} \left (a \cot \left (x \right )^{2}+b \cot \left (x \right ) \csc \left (x \right )+c \csc \left (x \right )^{2}\right ) y+k \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]

5857

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

5858

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

5859

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

5860

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

5861

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