5.4.1 Problems 1 to 100

Table 5.197: Problems solved by Maple only

#

ODE

Mathematica

Maple

Sympy

145

\[ {} \frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0 \]

204

\[ {} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0 \]

604

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

769

\[ {} \frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0 \]

796

\[ {} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0 \]

1755

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

2348

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

2523

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

2536

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

2912

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

2957

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

3002

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

3054

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

3056

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

3278

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

3279

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

3321

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

4111

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

4298

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

4390

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

4392

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

4434

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

4654

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

4811

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

5621

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

5622

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

5623

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

5630

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

5631

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

5636

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

5644

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

5648

\[ {} 8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y \]

5660

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

5664

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

5669

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

5675

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

5757

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

5760

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

5844

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

5855

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

5859

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

5881

\[ {} \left (\operatorname {a0} -\operatorname {a2} \operatorname {csch}\left (x \right )^{2}+4 \operatorname {a1} \sinh \left (x \right )^{2}\right ) y+\coth \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]

5882

\[ {} \left (\operatorname {a0} +4 \operatorname {a1} \cosh \left (x \right )^{2}-\operatorname {a2} \operatorname {sech}\left (x \right )^{2}\right ) y+\tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]

6176

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

6177

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

6179

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

6197

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

6229

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

6249

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

6261

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

6266

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

6268

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

6270

\[ {} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime } = 0 \]

6285

\[ {} -\left (a \left (a +1\right ) \left (1-x \right )+b^{2} x \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) x y^{\prime }+4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]

6301

\[ {} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}\right ) y+a^{2} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1-a^{2} \cos \left (x \right )^{2}\right ) y^{\prime \prime } = 0 \]

6325

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

6334

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

6354

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

6405

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

6406

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

6425

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

6539

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

6571

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

6575

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

6582

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

6583

\[ {} \operatorname {f5} y^{2}+\operatorname {f4} y y^{\prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime } = 0 \]

6595

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

6600

\[ {} h y^{2}+\operatorname {g1} y y^{\prime }+\operatorname {g0} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }+\operatorname {f0} {y^{\prime \prime }}^{2} = 0 \]

6603

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

6605

\[ {} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]

6608

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

6609

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

6681

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

6696

\[ {} 10 y^{\prime }+8 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime \prime } = 0 \]

6800

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

6930

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

7147

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

7318

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

7319

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

7320

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

7321

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

7475

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

7976

\[ {} {y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0 \]

8069

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

8070

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

8071

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

8265

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

8389

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

8424

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8425

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8426

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8427

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8715

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

8767

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

9053

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

9054

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

9199

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

9200

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

9761

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

9765

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