2.4.16 first order ode homog type D

Table 2.1081: first order ode homog type D [70]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

112

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

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

2.846

736

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

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

3.191

1243

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

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

3.560

1626

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

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

3.656

1645

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

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

3.974

2882

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

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

4.547

2883

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

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

5.877

2886

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

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

12.150

2888

\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\ y \left (6\right ) &= \pi \\ \end{align*}

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

6.251

2892

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

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

9.340

3555

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

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

3.671

3648

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

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

3.093

4243

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

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

3.874

4244

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

[[_homogeneous, ‘class D‘]]

2.564

4314

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

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

4.433

4315

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

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

4.079

4349

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

[[_homogeneous, ‘class D‘]]

2.633

4398

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

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

5.361

4404

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

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

4.339

4421

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

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

4.473

4440

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

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

4.733

4814

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

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

5.297

4816

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

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

7.047

4818

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

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

5.007

4819

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

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

4.289

4821

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

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

4.749

4824

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

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

4.869

4826

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

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

4.703

4831

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

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

7.065

6833

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

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

3.744

6898

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

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

3.622

6906

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

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

7.744

6907

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

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

6.809

7017

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

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

4.043

7254

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

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

4.467

7502

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

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

4.842

8697

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

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

5.450

8698

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

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

6.298

9017

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

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

4.777

9149

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

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

4.137

9150

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

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

4.333

10161

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

[[_homogeneous, ‘class D‘]]

3.796

11422

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

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

4.280

11424

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

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

4.745

11656

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

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

6.655

13975

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

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

6.382

13980

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

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

5.938

14467

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

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

4.757

15027

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

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

5.117

15453

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

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

4.100

16356

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

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

4.143

17910

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

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

5.636

19073

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

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

3.379

19278

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

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

9.281

19279

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

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

12.257

20248

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

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

3.753

20252

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

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

4.085

21807

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

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

118.658

22384

\begin{align*} y^{\prime }&=\frac {y+\cos \left (\frac {y}{x}\right )^{2}}{x} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}

[[_homogeneous, ‘class D‘]]

4.063

22389

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

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

3.851

22409

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

[[_homogeneous, ‘class D‘]]

3.239

22518

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

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

3.764

22537

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

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

3.858

22545

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

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

4.086

23209

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

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

5.092

23869

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

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

4.982

24163

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

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

8.738

24164

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

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

10.522

24166

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

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

96.438

24173

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

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

6.861