5.3.7 Problems 601 to 700

Table 5.47: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

4343

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

4350

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

4353

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

4354

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

4358

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

4360

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

4366

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

4374

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

4383

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

4384

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

4388

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

4389

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

4390

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

4391

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

4392

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

4393

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

4399

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

4402

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

4403

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

4406

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

4407

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

4410

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

4415

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

4417

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

4418

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

4424

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

4431

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

4432

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

4433

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

4434

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

4436

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

4441

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

4442

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

4460

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

4507

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

4512

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

4573

\[ {} \left [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )+\frac {{\mathrm e}^{3 t}}{{\mathrm e}^{2 t}+1}\right ] \]

4582

\[ {} [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )-2 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-6 x_{2} \left (t \right )+5 x_{3} \left (t \right )] \]

4629

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

4647

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

4648

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

4649

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

4653

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

4656

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

4657

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

4658

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

4661

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

4663

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

4664

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

4665

\[ {} y^{\prime } = a \,x^{n -1}+b \,x^{2 n}+c y^{2} \]

4666

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

4668

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

4669

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

4670

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

4677

\[ {} y^{\prime } = a \,x^{m}+b \,x^{n} y^{2} \]

4680

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

4683

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

4685

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

4686

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

4687

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

4696

\[ {} y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3} \]

4697

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

4699

\[ {} y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \]

4702

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

4707

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

4709

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

4711

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

4712

\[ {} y^{\prime }+f \left (x \right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) \cos \left (a y\right ) = 0 \]

4713

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

4714

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

4715

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

4724

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

4725

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

4728

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

4734

\[ {} y^{\prime } = x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right ) \]

4739

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

4740

\[ {} 2 y^{\prime }+a x = \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \]

4741

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

4756

\[ {} x y^{\prime } = a +b \,x^{n}+c y \]

4763

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

4765

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

4767

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

4768

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

4769

\[ {} x y^{\prime } = a \,x^{n}+b y+c y^{2} \]

4770

\[ {} x y^{\prime } = k +a \,x^{n}+b y+c y^{2} \]

4771

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

4778

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

4779

\[ {} x y^{\prime }+\operatorname {a0} +\operatorname {a1} x +\left (\operatorname {a2} +\operatorname {a3} x y\right ) y = 0 \]

4780

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

4781

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

4783

\[ {} x y^{\prime } = a \,x^{m}-b y-c \,x^{n} y^{2} \]

4786

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

4796

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

4797

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

4798

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

4799

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

4801

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

4804

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

4806

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

4807

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