4.1.41 Problems 4001 to 4100

Table 4.81: First order ode

#

ODE

Mathematica

Maple

Sympy

8439

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

8440

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

8441

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

8442

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

8443

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

8444

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

8445

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

8446

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

8447

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

8448

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

8449

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

8450

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

8451

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

8452

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

8453

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

8454

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

8455

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

8456

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

8457

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

8458

\[ {} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \]

8459

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

8460

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

8461

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

8462

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

8463

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

8464

\[ {} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \]

8465

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

8466

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

8467

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

8468

\[ {} x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0 \]

8469

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

8470

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

8471

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

8472

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

8473

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

8474

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

8475

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

8476

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

8477

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

8478

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

8479

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

8480

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

8481

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

8482

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

8483

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

8484

\[ {} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0 \]

8485

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

8486

\[ {} 5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \]

8487

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

8488

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

8533

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

8534

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

8535

\[ {} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0 \]

8536

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

8537

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

8538

\[ {} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0 \]

8539

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

8540

\[ {} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0 \]

8541

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

8542

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

8543

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

8544

\[ {} 16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0 \]

8545

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

8546

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

8547

\[ {} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1 = 0 \]

8548

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

8549

\[ {} x^{6} {y^{\prime }}^{2} = 16 y+8 x y^{\prime } \]

8550

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

8551

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

8552

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

8553

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

8554

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

8555

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

8556

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

8697

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

8698

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

8699

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

8700

\[ {} t x^{\prime }+2 x = 4 \,{\mathrm e}^{t} \]

8701

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

8702

\[ {} y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \]

8703

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

8704

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

8713

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

8714

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

8715

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

8716

\[ {} y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \]

8717

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

8718

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

8719

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

8720

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

8721

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

8722

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

8723

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

8724

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

8725

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

8726

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

8727

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

8728

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

8729

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

8730

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