5.1.4 Problems 301 to 400

Table 5.7: Problems not solved by Mathematica

#

ODE

Mathematica

Maple

Sympy

8427

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

8482

\[ {} x y^{\prime }-4 y = x^{6} {\mathrm e}^{x} \]

8664

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \]

8665

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right ) \]

8715

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

8767

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

8771

\[ {} y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0 \]

8772

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

8896

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

8897

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

9053

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

9054

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

9058

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

9123

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

9139

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

9199

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

9200

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

9214

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

9496

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

9497

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

9502

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

9503

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

9535

\[ {} y^{\prime \prime }+5 x y^{\prime }+y \sqrt {x} = 0 \]

9761

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

9765

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

9767

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

9793

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

9794

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

9810

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

9812

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

9828

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

9832

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

9984

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

10002

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

10017

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

10061

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

10062

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

10064

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

10132

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

10133

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

10136

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

10137

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

10141

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

10143

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

10166

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

10168

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

10207

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

10242

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

10270

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

10299

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

10344

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

10347

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

10360

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

10368

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

10369

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

10393

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

10444

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

10459

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

11361

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

11362

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

11363

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

11368

\[ {} y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right ) = 0 \]

11369

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

11387

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

11392

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

11395

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

11396

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

11432

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

11513

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

11515

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

11516

\[ {} y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a = 0 \]

11543

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

11546

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

11559

\[ {} \left (B x y+A \,x^{2}+a x +b y+c \right ) y^{\prime }-B g \left (x \right )^{2}+A x y+x \alpha +\beta y+\gamma = 0 \]

11562

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

11574

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

11647

\[ {} \left (\frac {\operatorname {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) = 0 \]

11756

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

11762

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

11781

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

11783

\[ {} x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0 \]

11804

\[ {} \left (\operatorname {b2} y+\operatorname {a2} x +\operatorname {c2} \right )^{2} {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {b0} y+\operatorname {a0} +\operatorname {c0} = 0 \]

11807

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

11808

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

11811

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

11832

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

12132

\[ {} y^{\prime } = -\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x} \]

12180

\[ {} y^{\prime } = -\frac {i \left (32 i x +64+64 y^{4}+32 x^{2} y^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 x^{4} y^{2}+x^{6}\right )}{128 y} \]

12189

\[ {} y^{\prime } = -\frac {i \left (i x +1+x^{4}+2 x^{2} y^{2}+y^{4}+x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4}+y^{6}\right )}{y} \]

12310

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

12314

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

12328

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

12363

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

12438

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

12486

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

12493

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

12515

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

12557

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

12584

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

12640

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