2.2.75 Problems 7401 to 7500

Table 2.163: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

7401

\begin{align*} x^{2}+2 y^{\prime } y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

6.987

7402

\begin{align*} y^{\prime }&=2 t \cos \left (y\right )^{2} \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

2.068

7403

\begin{align*} y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

2.917

7404

\begin{align*} y^{\prime }&=x^{2} \left (1+y\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

2.898

7405

\begin{align*} \sqrt {y}+\left (x +1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.318

7406

\begin{align*} y^{\prime }&={\mathrm e}^{x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

1.402

7407

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x^{2}}}{y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.496

7408

\begin{align*} y^{\prime }&=\sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

25.092

7409

\begin{align*} y^{\prime }&=2 y-2 t y \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

2.454

7410

\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ \end{align*}

[_quadrature]

2.036

7411

\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

4.134

7412

\begin{align*} y^{\prime }&=\left (x -3\right ) \left (1+y\right )^{{2}/{3}} \\ \end{align*}

[_separable]

5.408

7413

\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}

[_separable]

4.257

7414

\begin{align*} y^{\prime }&=x y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.233

7415

\begin{align*} y^{\prime }&=x y^{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

5.121

7416

\begin{align*} y^{\prime }&=x y^{3} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

5.177

7417

\begin{align*} y^{\prime }&=y^{2}-3 y+2 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}

[_quadrature]

1.043

7418

\begin{align*} x^{2} y^{\prime }+\sin \left (x \right )-y&=0 \\ \end{align*}

[_linear]

2.081

7419

\begin{align*} x^{\prime }+t x&={\mathrm e}^{x} \\ \end{align*}

[‘y=_G(x,y’)‘]

6.332

7420

\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=t y-y \\ \end{align*}

[_separable]

2.655

7421

\begin{align*} 3 t&={\mathrm e}^{t} y^{\prime }+y \ln \left (t \right ) \\ \end{align*}

[_linear]

4.210

7422

\begin{align*} x x^{\prime }+t^{2} x&=\sin \left (t \right ) \\ \end{align*}

[[_Abel, ‘2nd type‘, ‘class A‘]]

66.697

7423

\begin{align*} 3 r&=r^{\prime }-\theta ^{3} \\ \end{align*}

[[_linear, ‘class A‘]]

1.933

7424

\begin{align*} y^{\prime }-y-{\mathrm e}^{3 x}&=0 \\ \end{align*}

[[_linear, ‘class A‘]]

1.315

7425

\begin{align*} y^{\prime }&=\frac {y}{x}+2 x +1 \\ \end{align*}

[_linear]

0.945

7426

\begin{align*} r^{\prime }+r \tan \left (\theta \right )&=\sec \left (\theta \right ) \\ \end{align*}

[_linear]

1.513

7427

\begin{align*} y^{\prime } x +2 y&=\frac {1}{x^{3}} \\ \end{align*}

[_linear]

2.190

7428

\begin{align*} t +y+1-y^{\prime }&=0 \\ \end{align*}

[[_linear, ‘class A‘]]

0.962

7429

\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-4 x}-4 y \\ \end{align*}

[[_linear, ‘class A‘]]

2.476

7430

\begin{align*} y x^{\prime }+2 x&=5 y^{3} \\ \end{align*}

[_linear]

2.650

7431

\begin{align*} y^{\prime } x +3 y+3 x^{2}&=\frac {\sin \left (x \right )}{x} \\ \end{align*}

[_linear]

2.008

7432

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x -x&=0 \\ \end{align*}

[_separable]

1.941

7433

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-x^{2} y&=\left (x +1\right ) \sqrt {-x^{2}+1} \\ \end{align*}

[_linear]

4.154

7434

\begin{align*} y^{\prime }-\frac {y}{x}&=x \,{\mathrm e}^{x} \\ y \left (1\right ) &= {\mathrm e}-1 \\ \end{align*}

[_linear]

2.223

7435

\begin{align*} y^{\prime }+4 y-{\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= {\frac {4}{3}} \\ \end{align*}

[[_linear, ‘class A‘]]

2.368

7436

\begin{align*} t^{2} x^{\prime }+3 t x&=t^{4} \ln \left (t \right )+1 \\ x \left (1\right ) &= 0 \\ \end{align*}

[_linear]

1.819

7437

\begin{align*} y^{\prime }+\frac {3 y}{x}+2&=3 x \\ y \left (1\right ) &= 1 \\ \end{align*}

[_linear]

2.065

7438

\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=2 \cos \left (x \right )^{2} x \\ y \left (\frac {\pi }{4}\right ) &= -\frac {15 \sqrt {2}\, \pi ^{2}}{32} \\ \end{align*}

[_linear]

4.269

7439

\begin{align*} \sin \left (x \right ) y^{\prime }+y \cos \left (x \right )&=x \sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}

[_linear]

2.525

7440

\begin{align*} y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}}&=x \\ y \left (0\right ) &= 2 \\ \end{align*}

[_linear]

2.342

7441

\begin{align*} \left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1&=0 \\ \end{align*}

[[_1st_order, _with_exponential_symmetries]]

7.278

7442

\begin{align*} 2 y+y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}

[_rational, _Bernoulli]

1.809

7443

\begin{align*} y^{\prime }+\frac {3 y}{x}&=x^{2} \\ \end{align*}

[_linear]

2.552

7444

\begin{align*} x^{\prime }&=\alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \\ x \left (0\right ) &= x_{0} \\ \end{align*}

[[_linear, ‘class A‘]]

2.442

7445

\begin{align*} u^{\prime }&=\alpha \left (1-u\right )-\beta u \\ \end{align*}

[_quadrature]

0.864

7446

\begin{align*} x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime }&=0 \\ \end{align*}

[_linear]

2.211

7447

\begin{align*} x^{{10}/{3}}-2 y+y^{\prime } x&=0 \\ \end{align*}

[_linear]

3.062

7448

\begin{align*} \sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.199

7449

\begin{align*} y \,{\mathrm e}^{y x}+2 x +\left (x \,{\mathrm e}^{y x}-2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

0.188

7450

\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

0.161

7451

\begin{align*} y^{2}+\left (2 y x +\cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

0.155

7452

\begin{align*} 2 x +y \cos \left (y x \right )+\left (x \cos \left (y x \right )-2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

0.218

7453

\begin{align*} \theta r^{\prime }+3 r-\theta -1&=0 \\ \end{align*}

[_linear]

0.172

7454

\begin{align*} 2 y x +3+\left (x^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}

[_linear]

0.105

7455

\begin{align*} \left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

0.349

7456

\begin{align*} \cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

7.289

7457

\begin{align*} {\mathrm e}^{t} \left (y-t \right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime }&=0 \\ \end{align*}

[_linear]

0.201

7458

\begin{align*} \frac {t y^{\prime }}{y}+1+\ln \left (y\right )&=0 \\ \end{align*}

[_separable]

0.312

7459

\begin{align*} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta }&=0 \\ \end{align*}

[_linear]

0.164

7460

\begin{align*} y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

0.255

7461

\begin{align*} \frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational]

0.156

7462

\begin{align*} 2 x +y^{2}-\cos \left (x +y\right )+\left (2 y x -\cos \left (x +y\right )-{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

27.799

7463

\begin{align*} 2 x +\frac {y}{y^{2} x^{2}+1}+\left (\frac {x}{y^{2} x^{2}+1}-2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_exact, _rational]

2.194

7464

\begin{align*} \frac {2}{\sqrt {-x^{2}+1}}+y \cos \left (y x \right )+\left (x \cos \left (y x \right )-\frac {1}{y^{{1}/{3}}}\right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

6.410

7465

\begin{align*} \frac {1}{x}+2 x y^{2}+\left (2 x^{2} y-\cos \left (y\right )\right ) y^{\prime }&=0 \\ y \left (1\right ) &= \pi \\ \end{align*}

[_exact]

2.969

7466

\begin{align*} y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_exact]

3.542

7467

\begin{align*} y \,{\mathrm e}^{t}+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0 \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

3.500

7468

\begin{align*} {\mathrm e}^{t} x+1+\left ({\mathrm e}^{t}-1\right ) x^{\prime }&=0 \\ x \left (1\right ) &= 1 \\ \end{align*}

[_linear]

1.944

7469

\begin{align*} \sin \left (x \right ) y^{2}+\left (\frac {1}{x}-\frac {y}{x}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 1 \\ \end{align*}

[_separable]

4.931

7470

\begin{align*} \tan \left (y\right )-2+\left (x \sec \left (y\right )^{2}+\frac {1}{y}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

34.220

7471

\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

3.470

7472

\begin{align*} 5 x^{2} y+6 x^{3} y^{2}+4 x y^{2}+\left (2 x^{3}+3 x^{4} y+3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

21.032

7473

\begin{align*} 2 x +\frac {y}{x}+\left (y x -1\right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

2.160

7474

\begin{align*} 2 y^{3}+2 y^{2}+\left (3 x y^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

0.596

7475

\begin{align*} \left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5.128

7476

\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

3.360

7477

\begin{align*} x^{2} \sin \left (x \right )+4 y+y^{\prime } x&=0 \\ \end{align*}

[_linear]

2.183

7478

\begin{align*} 2 x y^{2}-y+y^{\prime } x&=0 \\ \end{align*}

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

3.739

7479

\begin{align*} 2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6.356

7480

\begin{align*} 3 x^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

2.144

7481

\begin{align*} x^{4}-x +y-y^{\prime } x&=0 \\ \end{align*}

[_linear]

1.654

7482

\begin{align*} 2 y^{2}+2 y+4 x^{2}+\left (2 y x +x \right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

2.692

7483

\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

3.368

7484

\begin{align*} 2 x y^{3}+1+\left (3 y^{2} x^{2}-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

2.733

7485

\begin{align*} 2 y^{2}-6 y x +\left (3 y x -4 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7.168

7486

\begin{align*} 3 y+2 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5.943

7487

\begin{align*} 3+y+y x +\left (3+x +y x \right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

4.940

7488

\begin{align*} 2 x +2 y+2 x^{3} y+4 y^{2} x^{2}+\left (2 x +x^{4}+2 x^{3} y\right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

17.310

7489

\begin{align*} 2 t x x^{\prime }+t^{2}-x^{2}&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7.367

7490

\begin{align*} \left (y-4 x -1\right )^{2}-y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _Riccati]

7.717

7491

\begin{align*} y^{\prime }+\frac {y}{x}&=x^{3} y^{2} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

4.421

7492

\begin{align*} \left (t +x+2\right ) x^{\prime }+3 t -x-6&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

29.697

7493

\begin{align*} -y+t y^{\prime }&=\sqrt {t y} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10.931

7494

\begin{align*} y \,{\mathrm e}^{-2 x}+y^{3}-{\mathrm e}^{-2 x} y^{\prime }&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Bernoulli]

2.708

7495

\begin{align*} \cos \left (x +y\right ) y^{\prime }&=\sin \left (x +y\right ) \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

1.875

7496

\begin{align*} y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

0.247

7497

\begin{align*} y x +y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

3.687

7498

\begin{align*} 3 x^{2}-y^{2}-\left (y x -\frac {x^{3}}{y}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18.833

7499

\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

3.780

7500

\begin{align*} x^{2}+y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

6.492