### 3 Lookup table of results

 Table 5: Breakdown of results for each PDE. Time in seconds # PDE description Mathematica Maple hand solved? result time result time 1 Linear PDE, the transport equation ✓ 0.003 ✓ 0.12 Yes 2 Linear PDE ✓ 0.003 ✓ 0.01 Yes 3 Linear PDE, initial value problem ✓ 0.013 ✓ 0.12 Yes 4 Initial-boundary value problem ✓ 0.046 ✓ 0.25 Yes 5 Linear PDE, the transport equation with initial conditions ✓ 0.003 ✓ 0.01 Yes 6 First order wave PDE, with initial conditions (Haberman 12.2.2) ✓ 0.003 ✓ 0.01 Yes 7 First order wave PDE, with initial and boundary conditions (Haberman 12.2.4) ✗ 45.343 ✓Solution contains unresolved invlaplace calls 0.23 Yes 8 First order wave PDE, with initial conditions, non homogeneous (Haberman 12.2.5 (a)) ✓ 0.027 ✓ 0.03 Yes 9 First order wave PDE, with initial conditions, non homogeneous (Haberman 12.2.5 (d)) ✓ 0.018 ✓ 0.05 Yes 10 General solution for a quasilinear ﬁrst-order PDE ✓ 0.05 ✓ 0.04 Yes 11 quasilinear ﬁrst-order PDE, scalar conservation law ✓Implicit solution 0.029 ✓ 0.01 Yes 12 quasilinear ﬁrst-order PDE, scalar conservation law with initial value ✓ 0.007 ✓ 0.02 Yes 13 nonlinear ﬁrst-order PDE, the Clairaut equation ✓ 0.024 ✓ 0.08 Yes 14 nonlinear ﬁrst-order PDE, the Clairaut equation with initial value ✓ 0.01 ✓ 0.58 No 15 Another example of nonlinear Clairaut equation ✓ 0.021 ✓ 0.01 No 16 Recover a function from its gradient vector ✓ 0.014 ✓ 0.05 No 17 General solution of a ﬁrst order nonlinear PDE ✗ 0.095 ✓Has unresolved integral in the answer 0.03 No 18 Nonlinear ﬁrst order PDE ✓ 0.086 ✓ 0.43 No 19 ﬁrst order PDE of three unknowns ✗ (Timed out) 600. ✓ 1.75 No 20 left and right end temperature ﬁxed at zero. No source (Haberman 2.3.3 (a)) ✓ 0.277 ✓ 1.67 Yes 21 left and right end temperature ﬁxed at zero, No source (Haberman 2.3.3 (b)) ✓ 0.727 ✓ 1.78 Yes 22 left and right end temperature ﬁxed at zero, No source (Haberman 2.3.3 (c)) ✓but $$n=3$$ should be special case 0.734 ✓handled $$n=3$$ case correctly. 3.46 Yes 23 left and right end temperature ﬁxed at zero, No source (Haberman 2.3.3 (d)) ✓ 0.945 ✓ 1.71 Yes 24 left and right end insulated, No source (Haberman 2.3.7) ✓ 0.299 ✓ 0.68 Yes 25 left and right end ﬁxed at zero, with heat sink (Haberman 2.3.8) ✗ 31.203 ✓ 0.8 Yes 26 left and right end insulated, No source (Haberman 2.4.1 (a)) ✓ 0.438 ✓ 1.26 No 27 left and right end insulated, No source (Haberman 2.4.1 (b)) ✓ 0.303 ✓ 2.12 Yes 28 left and right end insulated, No source (Haberman 2.4.1 (c)) ✓ 0.651 ✓ 3.43 Yes 29 left and right end insulated, No source (Haberman 2.4.1 (d)) ✓ 0.267 ✓ 1.9 No 30 left and insulated, right end ﬁxed at zero. No source (Haberman 2.4.2) ✓ 0.217 ✓ 0.87 Yes 31 Left end insulated, right end has convection heat loss, No source ✗ 30.397 ✓ 1.81 No 32 Periodic boundary conditions, No source ✗ 0.388 ✓ 9.76 No 33 Left and right end have Robin boundary conditions. No source ✗ 31.391 ✓ 2.45 No 34 with domain from -1 to +1, both ends ﬁxed at zero temperature. no source ✗ 30.507 ✓ 0.9 No 35 Left and right end ﬁxed at non-zero temperature, zero intial conditions, no source term ✓ 13.626 ✓ 0.44 No 36 Left held at constant non-zero temperature, right nonhomogeneous Neumann, No source (Haberman 8.2.1 (a)) ✗ 0.539 ✓ 0.99 Yes 37 Left and right end ﬁxed at constant non-zero temperature, non zero intial conditions, with source term that is constant (Haberman 8.2.1 (d)) ✗ 44.45 ✓ 0.67 Yes 38 Left and right end ﬁxed zero temperature, non zero intial conditions, internal source term present ✗ 0.731 ✓ 0.73 No 39 Left and right end ﬁxed zero temperature, non zero intial conditions, internal source term present ✓ 0.373 ✓ 1.05 No 40 Left and right end ﬁxed zero temperature, intial conditions is hat function, No source ✓ 18.612 ✓ 1.06 No 41 Left and right end ﬁxed zero temperature, intial conditions non zero at single location, No source ✓ 5.314 ✓ 0.42 No 42 Left temperature depends on time, right end ﬁxed at zero. zero initial conditions, No source ✓ 6.127 ✓ 0.81 No 43 Left and right end ﬁxed at zero temperature. non zero initial conditions, external source depends on space only (Haberman 8.2.1 (f)) ✗ 0.363 ✓ 1.48 No 44 Left and right end ﬁxed at zero temperature. non zero initial conditions, external source depends on time only (Pinchover and Rubinstein 6.25) ✗ 0.784 ✓ 3.32 No 45 Left and right end ﬁxed at zero temperature. non zero initial conditions, external source depends on time and space ✗ 0.378 ✓ 13.73 No 46 Left and right end insulated. non zero initial conditions, external source depends on time and space (Pinchover and Rubinstein 6.17) ✗ 1.354 ✓ 1.99 No 47 Left end insulated, right end non-homogeneous Neumann boundary condition, no source ✗ 0.276 ✓ 2.79 No 48 Left and right end ﬁxed at zero, source depends on time and space (Pinchover and Rubinstein 6.23) ✓ 0.861 ✓ 36.94 No 49 Left and right end insulated, source depends on time and space (Pinchover and Rubinstein 6.21) ✓ 0.264 ✓ 1.6 No 50 Left and right end nonhomogeneous Dirichlet BC that depends on time, source that depends on space ✗ 30.598 ✓ 3.82 No 51 Left and right end ﬁxed at zero, non zero initial conditions, source that depends on time and space ✗ 1.546 ✓ 4.69 No 52 Left end held ﬁxed at constant temperature, right end at zero. Zero initial conditions, source that depends on time and space (Haberman 8.3.6) ✗ 30.671 ✓ 18.43 Yes 53 Both left and right end nonhomogeneous Neumann condition which is function of time, source that depends on time and space (Haberman 8.2.2. (a)) ✗ 0.408 ✓ 3.4 Yes 54 left and right end nonhomogeneous held at ﬁxed temperature, No source (Articolo 8.4.1) ✓ 15.249 ✓ 0.54 No 55 left end held at ﬁxed temperature, right end Robin BC, with source that depends on time (Articolo 8.4.3) ✗ 30.735 ✓ 600. No 56 left end insulated, right end set at ﬁxed ﬂux with no source ✗ 14.523 ✓ 1.9 No 57 non zero heat ﬂux at both ends, and no source ✗ 30.582 ✓ 3.99 Yes 58 Left end $$u(0,t)=f(t)$$, zero initial conditions, No source (Logan p. 76) ✓ 0.27 ✓ 0.51 No 59 Left end $$u(0,t)=1$$, zero initial conditions, No source ✓ 1.548 ✓ 0.12 No 60 B.C. not located at $$x=0$$ and I.C. not at $$t=0$$ ✗due to IC/BC not zero 0.007 ✓ 0.5 No 61 Left end at $$u(0,t)=\mu$$, non zero initial conditions, No source ✓ 2.121 ✓ 0.13 No 62 No condition on left end. Initial conditions given, no source ✓ 1.16 ✓ 0.3 No 63 With advection term and initial conditons ✓ 0.361 ✓ 0.25 No 64 Initial position as a UnitBox function ✓ 1.601 ✓ 0.41 No 65 Left end ﬁxed at speciﬁc temperature, non-zero initial conditions, no source ✓ 8.027 ✓ 1.56 No 66 Left end function of temperature, zero initial conditions, no source ✓ 2.31 ✓ 0.73 No 67 Left end insulated, initial conditions triangle function. No source ✓ 27.184 ✓ 0.78 No 68 one end insulated at arbitray location, initial conditions not at $$t=0$$. No source ✗ 0.009 ✓ 0.62 No 69 No boundary conditions speciﬁed. Initial conditions $$u(x,0)=\sin (x)$$ and no source ✓ 5.638 ✓ 0.25 No 70 No intial conditions and no boundary conditions speciﬁed ✗ 0.002 ✓ 0.05 No 71 with source and a piecewise initial condition at $$t>0$$ ✗due to i.c. not at zero 0.012 ✓ 0.91 No 72 4 edges are ﬁxed at zero temperature, No source ✗ 0.004 ✓ 1.87 No 73 2 edges are ﬁxed at zero temperature, 2 edges are insulated, internal source term ✗ 0.003 ✓ 1.81 No 74 Rectangle plate, losing heat by convection (Articolo 6.6.3) ✗ 0.804 ✓ 2.44 No 75 circumference ﬁxed at zero temperature, no $$\theta$$ dependency, No source ✓ 1.407 ✓But has unresolved inverse Laplace transforms 0.45 No 76 circumference ﬁxed at zero temperature, no $$\theta$$ dependency, zero initial conditions, source that depends on time and radius (Haberman 8.3.5) ✗ 0.004 ✗ 0.08 Yes 77 Articolo example 6.9.1. On quarter disk, homogeneous BC (Articolo 6.9.1) ✗ 0.004 ✓ 10.87 No 78 On half disk, homogeneous BC (Articolo 6.9.2) ✗ 0.003 ✓ 5.19 No 79 Inside disk with time-independent boundary conditions and $$\theta$$ dependency (Haberman 8.2.5) ✗ 0.003 ✗ 0.56 Yes 80 using growth form for reaction term ✗ 22.728 ✓ 0.55 No 81 using logistic form for reaction term ✗ 1.189 ✗ 4.94 No 82 using Aleee form for reaction term ✗ 2.236 ✗ 9.1 No 83 Laplace PDE inside rectangle (Haberman 2.5.1 (a)) ✓ 0.187 ✓ 14.11 No 84 Laplace PDE inside rectangle (Haberman 2.5.1 (b)) ✓ 0.167 ✓ 13.62 No 85 Laplace PDE inside rectangle (Haberman 2.5.1 (c)) ✗ 0.282 ✓ 15.39 No 86 Laplace PDE inside rectangle (Haberman 2.5.1 (d)) ✗ 0.284 ✓ 13.03 No 87 Laplace PDE inside rectangle (Haberman 2.5.1 (e)) ✗ 0.564 ✓ 21.5 Yes 88 Laplace PDE inside rectangle, top/bottom edges non-zero ✓ 2.092 ✓ 2.72 No 89 Laplace PDE inside rectangle, top edge at inﬁnity ✗May be there is workaround. 1.552 ✓ 1.21 No 90 Laplace PDE in 2D Cartessian with boundary condition as Dirac function ✓ 0.039 ✓ 0.33 No 91 Laplace PDE in rectangle, one side homogeneous and 3 sides are not ✓ 0.517 ✓ 13.33 No 92 Laplace PDE example 18 from Maple help page ✓ 33.074 ✓ 0.33 No 93 Laplace PDE on rectangle with one edge at inﬁnity ✗ 1.434 ✓ 5.52 No 94 Laplace PDE inside a disk, periodic boundary conditions ✓ 0.134 ✓ 1.1 No 95 Dirichlet problem for the Laplace equation in upper half plan ✓ 1.564 ✓used convert(sol,Int) 0.76 No 96 Dirichlet problem for the Laplace equation in right half-plane: ✓ 25.382 ✓ 0.1 No 97 Dirichlet problem for the Laplace equation in the ﬁrst quadrant ✓ 24.952 ✗ 2.56 No 98 Neumann problem for the Laplace equation in the upper half-plane ✓ 13.069 ✓used convert(sol,Int). 0.35 No 99 Dirichlet problem for the Laplace equation in a rectangle ✓ 1.2 ✓ 1.22 No 100 Cartessian coordinates with boundary conditions on two sides only ✗ 0.211 ✓ 1.14 No 101 in Rectangle, right edge at inﬁnity ✗ 1.404 ✓ 4.7 No 102 Laplace PDE inside quarter disk, Neumann BC at edge ✗ 1.429 ✓ 1.28 No 103 Laplace PDE inside quarter-circle (Haberman 2.5.5 (c)) ✗ 1.168 ✓ 0.5 Yes 104 Laplace PDE inside semi-circle ✗ 1.462 ✓ 0.56 Yes 105 Laplace PDE inside circular annulus, Neumann boundary conditions using unspeciﬁed functions (Haberman 2.5.8 (b)) ✗ 0.009 ✓But has unresolved Invfourier and Fourier calls 4.33 No 106 Laplace PDE inside circular annulus, Dirichlet boundary conditions using speciﬁed functions ✓ 1.312 ✓ 0.93 No 107 Laplace PDE outside a disk, periodic boundary conditions ✗ 0.007 ✓ 0.96 No 108 Laplace in a sphere ✗ 0.02 ✓ 0.57 No 109 Poisson equation in a rectangle, all boundaries are zero ✗ 0.007 ✗ 9.23 Yes 110 Dirichlet problem for the Poisson equation in a rectangle ✓ 0.167 ✓ 0.1 No 111 Dirichlet problem for the Helmholtz equation in a rectangle ✓ 2.193 ✓ 3.34 No 112 With no boundary conditions speciﬁed ✗why? It solved earlier with BC? 0.004 ✓ 0.04 No 113 Inside square ✗ 0.723 ✓ 12.15 No 114 With zero initial position and velocity, and with source term (Logan p. 115) ✓ 0.131 ✓ 0.25 No 115 Both ends ﬁxed, zero initial position, non-zero initial velocity, with extra term present ✗ 8.824 ✓ 1.02 No 116 One end ﬁxed, another free, both initial conduitions non zero, and source that depends on time and space ✗ 0.786 ✓ 39.93 No 117 Both ends ﬁxed, no initial conduitions give and no source (Logan p. 28) ✗ 0.237 ✓ 0.3 No 118 One end ﬁxed, other free, initial position not zero, initial velocity zero, no source (Logan p. 130) ✗ 0.599 ✓ 3.19 No 119 Both ends ﬁxed end, initial conditions zero, with source as generic function that depends on time and space (Logan p. 149) ✗ 0.769 ✓ 1.06 No 120 Both ends ﬁxed end, initial position given, zero initial velocity, with source that depends on time and space (Haberman 8.5.2 (a)) ✗ 0.806 ✓ 6.3 No 121 Both ends ﬁxed end, initial position given, zero initial velocity, with source that depends on time and space (Haberman 8.5.2 (b)) ✗ 1.094 ✓ 25.2 Yes 122 Both ends ﬁxed, initial conditions both not zero, No source ✓ 36.008 ✓ 1.72 No 123 Both ends ﬁxed end, initial conditions both not zero, and with constant source ✗ 0.657 ✓ 4.4 No 124 Both ends ﬁxed end, with source (Logan p. 213) ✗ 0.646 ✓ 3.7 No 125 Telegraphy PDE, both ends ﬁxed with damping ✗ 31.252 ✓But $$n = 1$$ should not be included. 1.76 No 126 Both ends ﬁxed. Initial velocity zero. Dispersion term present ✗Due to adding dispersion term 31.301 ✓ 8.06 No 127 Both ends ﬁxed, non-zero initial position ✓But sum should not include $$n=2$$ 30.945 ✓Handled $$n=2$$ case correctly 7.5 No 128 Both ends ﬁxed, zero initial position, non zero initial velocity, with source that depends on time and space ✗ 26.205 ✓ 7.44 No 129 Left end ﬁxed, right end oscillates, initially at rest. With source that depends on time and space ✗ 30.668 ✓ 7.64 No 130 Left end having a moving boundary condition ✓ 6.524 ✓ 0.34 No 131 Initial value with a Dirichlet condition on the half-line ✓ 23.231 ✓ 2.05 No 132 Initial value problem with a Neumann condition on the half-line ✓ 12.001 ✓ 0.42 No 133 With initial conditions given at $$t=1$$ instead of $$t=0$$ ✓ 22.004 ✓ 0.24 No 134 initial conditions at $$t=0$$ but B.C. at $$x=1$$ ✗ 9.092 ✓ 0.34 No 135 initial conditions at $$t=1$$ with source that depends on time and space ✗ 0.008 ✓ 1.62 No 136 Left end free with initial position and velocity given ✓ 0.13 ✓ 0.18 No 137 General solution for a second-order hyperbolic PDE on real line ✓ 0.003 ✓ 0.15 No 138 With initial conditions speciﬁed, no source ✓ 0.044 ✓ 0.06 No 139 Wave PDE on inﬁnite domain with initial conditions speciﬁed, with source term ✓ 0.009 ✓ 0.08 No 140 non-linear wave PDE (Solitons) ✓ 0.042 ✓Returning a solution that is not the most general one 0.11 No 141 Hyperbolic PDE with non-rational coeﬃcients ✓ 0.108 ✗ 0.07 No 142 Inhomogeneous hyperbolic PDE with constant coeﬃcients ✓ 0.003 ✓ 0.08 No 143 system of 2 inhomogeneous linear hyperbolic system with constant coeﬃcients ✓ 0.268 ✗ 0.26 No 144 In square, given initial position but with zero initial velocity ✗ 0.003 ✓ 5.16 No 145 In square with damping. Given zero initial position but with non-zero initial velocity ✗ 0.003 ✓ 12.52 No 146 In rectangle. All 4 edges are ﬁxed and given non-zero initial position with zero initial velocity ✓ 0.805 ✓ 2.43 No 147 In rectangle. All 4 edges are ﬁxed and given non-zero initial position with zero initial velocity (Haberman 8.5.5 (a)) ✗ 0.003 ✗ 0.11 No 148 In circular disk. ﬁxed edge of disk, no $$\theta$$ dependency, with initial position and velocity given ✓ 30.994 ✓Has unresolved Invlaplace calls 31.93 No 149 In circular disk. ﬁxed edge of disk, with $$\theta$$ dependency, zero initial velocity ✗ 0.004 ✗ 0.18 No 150 No initial and no boundary conditions given ✗ 0.029 ✓ 0.99 No 151 No initial and no boundary conditions given ✗ 0.003 ✓ 0.2 No 152 Schrodinger PDE with zero potential (Logan p. 30) ✓ 0.251 ✓ 0.43 No 153 Schrodinger PDE with initial and boundary conditions. Zero potential ✓ 0.013 ✓ 4.12 No 154 Initial value problem with Dirichlet boundary conditions. Zero potential ✓ 0.728 ✓ 1.12 No 155 Solve a Schrodinger equation with potential over the whole real line ✓ 0.004 ✗Maple does not support $$\infty$$ in boundary conditions 0. No 156 Schrodinger equation, with initial conditions. Zero potential (Griﬃths p. 47) ✓ 35.591 ✓ 1.18 No 157 Schrodinger equation, with initial conditions. Inﬁnite square well potential (Griﬃths p. 47) ✓ 0.01 ✓ 0.49 No 158 In 2 space dimensions ✗ 0.653 ✓ 4.95 No 159 Beam PDE with zero initial velocity ✓ 0.19 ✓ 0.11 No 160 viscous ﬂuid ﬂow with no initial conditions ✓ 0.029 ✓ 0.1 No 161 viscous ﬂuid ﬂow with initial conditions ✓ 7.325 ✗ 0.6 No 162 viscous ﬂuid ﬂow with initial conditions as UnitBox ✓ 11.369 ✗ 0.7 No 163 classic Black Scholes model from ﬁnance, European call version ✓ 2.939 ✓ 0.61 No 164 Boundary value problem for the Black Scholes equation ✓ 1.026 ✓ 1.87 No 165 Korteweg-deVries (waves on shallow water surfaces) with no initial conditions ✓ 0.036 ✓ 0.11 No 166 Boundary value problem for the Tricomi equation ✓ 5.243 ✓ 2.91 No 167 Cauchy Riemann PDE with Prescribe the values of $$u$$ and $$v$$ on the $$x$$ axis ✓ 0.003 ✓ 0.23 No 168 Cauchy Riemann PDE With extra term on right side ✗ 0.001 ✓ 0.08 No 169 Hamilton-Jacobi type PDE ✗ 0.05 ✓ 0.23 No 170 A second order PDE ✗ 0.034 ✓ 0.06 No 171 second order PDE in Polar coordinates ✗ 0.011 ✓ 0.46 No 172 Laplace like PDE with polynomial solution ✓ 4.571 ✓ 1.34 No 173 Third oder PDE ✗ 0.271 ✓ 12.38 No 174 PDE solved by Laplace transform ✗ 0.181 ✓ 0.29 No 175 Linear PDE, initial conditions at $$t=1$$ ✗ 0.003 ✓ 0.46 No 176 Linear PDE, initial conditions at $$t=t_0$$ ✗ 0.003 ✓ 0.32 No 177 second order in time, Linear PDE, initial conditions at $$t=t_0$$ ✗ 0.003 ✓ 0.45 No 178 Einstein-Weiner PDE ✗ 0.003 ✓ 0.2 No 179 Bateman-Burgers equation ✓ 0.019 ✓ 0.11 No 180 Benjamin Bona Mahony ✓ 0.03 ✓ 0.12 No 181 Benjamin Ono ✓ 0.018 ✓ 0.11 No 182 Born Infeld ✓ 0.007 ✓Mathematica’s solution is simpler. Veriﬁed both correct. 0.23 No 183 Boussinesq ✓ 0.039 ✓ 0.13 No 184 Boussinesq type PDE ✓ 0.038 ✓ 0.15 No 185 Buckmaster ✗ 0.062 ✓Answer in terms of RootOf. 0.57 No 186 Camassa Holm ✗ 0.171 ✓Answer in terms of RootOf. 2. No 187 Chaﬀee Infante equation ✗ 0.087 ✓ 0.28 No 188 Clarke’s equation ✗ 0.009 ✗ 0.04 No 189 Degasperis Procesi ✗ 0.166 ✓But still has unresolved ODE’s in solution 0.58 No 190 Dym equation ✗ 0.081 ✓has RootOf 0.48 No 191 Estevez Mansﬁeld Clarkson equation ✓ 0.031 ✓ 0.19 No 192 Fisher’s equation ✓ 0.048 ✓ 0.26 No 193 Hunter Saxton ✗ 0.042 ✓with RootOf 0.14 No 194 Kadomtsev Petviashvili ✓ 0.067 ✓ 0.18 No 195 Klein Gordon (nonlinear) ✗ 0.004 ✗ 0.05 No 196 special case Klein Gordon (nonlinear) ✗ 0.211 ✓ 0.65 No 197 Khokhlov Zabolotskaya ✗ 0.056 ✓ 0.42 No 198 Korteweg de Vries (KdV) ✓ 0.013 ✓ 0.07 No 199 Lin Tsien equation ✗ 0.07 ✓ 0.41 No 200 Liouville equation ✗ 0.003 ✗ 0.04 No 201 Plateau ✗ 0.031 ✓ 0.27 No 202 Rayleigh ✗ 0.074 ✓Has RootOf 0.18 No 203 Sawada Kotera ✓ 0.081 ✓ 0.27 No 204 Sine Gordon ✗ 0.007 ✗ 0.02 No 205 Sinh Gordon ✗ 0.007 ✗ 0.01 No 206 Sinh Poisson ✗ 0.014 ✗ 0.01 No 207 Thomas equation ✗ 0.061 ✓ 0.5 No 208 phi equation ✓ 0.041 ✓ 0.26 No 209 problem number 1 ✓ 0.021 ✓ 0.01 No 210 problem number 2 ✓ 0.02 ✓ 0. No 211 problem number 3 ✓ 0.022 ✓ 0. No 212 problem number 4 ✓ 0.019 ✓ 0. No 213 problem number 5 ✓ 0.31 ✓ 0.01 No 214 problem number 6 ✓ 0.315 ✓ 0.01 No 215 problem number 1 ✓ 0.003 ✓Solution missing $$a,b$$ compared to book, but technically still correct. 0. Yes 216 problem number 2 ✓ 0.005 ✓ 0.02 Yes 217 problem number 3 ✓ 0.018 ✓ 0.03 Yes 218 problem number 4 ✓ 0.005 ✓ 0.02 Yes 219 problem number 5 ✓ 0.008 ✓ 0.08 No 220 problem number 6 ✓ 0.06 ✓ 0.09 No 221 problem number 7 ✓ 0.021 ✓But Mathematica solution is simpler, both veriﬁed correct 0.75 No 222 problem number 8 ✗ 1.783 ✓ 1.08 No 223 problem number 1 ✓ 0.005 ✓ 0.01 No 224 problem number 2 ✓ 0.09 ✓ 0.1 No 225 problem number 3 ✓ 0.028 ✓ 0.02 No 226 problem number 4 ✓ 0.191 ✓ 0.1 No 227 problem number 5 ✓ 0.076 ✓ 0.14 No 228 problem number 6 ✓ 0.138 ✓ 0.1 No 229 problem number 7 ✓ 0.153 ✓ 0.94 No 230 problem number 8 ✓ 0.222 ✓ 0.17 No 231 problem number 9 ✓ 0.071 ✓ 0.2 No 232 problem number 10 ✓ 0.044 ✓ 0.08 No 233 problem number 11 ✓ 0.117 ✓ 0.06 No 234 problem number 12 ✓ 0.282 ✓ 0.26 No 235 problem number 13 ✓ 0.009 ✓ 0.03 No 236 problem number 14 ✓ 0.028 ✓ 0.25 No 237 problem number 15 ✓ 0.168 ✓ 0.19 No 238 problem number 16 ✓ 0.817 ✓ 0.18 No 239 problem number 17 ✓ 0.527 ✓ 0.3 No 240 problem number 18 ✓ 0.023 ✓ 0.06 No 241 problem number 19 ✓ 0.071 ✓ 0.14 No 242 problem number 20 ✗ 0.05 ✓ 0.22 No 243 problem number 21 ✓ 0.05 ✓ 0.13 No 244 problem number 22 ✓ 0.099 ✓ 0.37 No 245 problem number 23 ✓ 0.033 ✓ 0.21 No 246 problem number 24 ✗ 0.064 ✓ 0.16 No 247 problem number 25 ✗ (Timed out) 600. ✗ (Timed out) 600. No 248 problem number 26 ✗ 268.926 ✗ 29.33 No 249 problem number 27 ✗ 101.494 ✗ 2.1 No 250 problem number 28 ✗ 0.07 ✓solution contains RootOf 0.2 No 251 problem number 29 ✗ 101.088 ✗ 1.12 No 252 problem number 30 ✗ 0.066 ✓ 0.16 No 253 problem number 31, Hesse’s equation ✗ 235.962 ✓ 8.47 No 254 problem number 1 ✓But it can’t solve it when assuming $$b>0$$ which is strange. 0.065 ✓Mathematica solution is much simpler 1.62 No 255 problem number 2 ✓ 0.093 ✓ 0.12 No 256 problem number 3 ✓ 0.06 ✓ 0.74 No 257 problem number 4 ✗ 0.089 ✓ 0.81 No 258 problem number 5 ✗ 0.373 ✓Answer contains RootOf 0.12 No 259 problem number 6 ✗ 0.071 ✓Answer contains RootOf 0.05 No 260 problem number 7 ✓ 0.04 ✓ 0.11 No 261 problem number 8 ✓ 0.017 ✓ 0.05 No 262 problem number 9 ✗ (Timed out) 600. ✓ 0.04 No 263 problem number 1 ✓ 0.018 ✓ 0.02 No 264 problem number 2 ✓ 0.118 ✓ 0.2 No 265 problem number 3 ✓ 0.224 ✓ 0.19 No 266 problem number 4 ✓ 0.182 ✓ 0.92 No 267 problem number 5 ✗ 0.188 ✗ (Timed out) 600. No 268 problem number 6 ✓ 1.7 ✓ 0.41 No 269 problem number 7 ✗ 1.046 ✓ 2.01 No 270 problem number 1 ✓ 0.031 ✓ 0.12 No 271 problem number 2 ✓ 0.095 ✓ 0.28 No 272 problem number 3 ✓ 0.03 ✓ 0.1 No 273 problem number 4 ✗ 20.325 ✓ 0.91 No 274 problem number 5 ✓ 0.336 ✓ 0.3 No 275 problem number 6 ✗ (Timed out) 600. ✓ 1.48 No 276 problem number 7 ✓ 0.101 ✓ 0.13 No 277 problem number 8 ✗ 22.769 ✓ 2.1 No 278 problem number 9 ✗ 0.921 ✓ 3.27 No 279 problem number 10 ✗ (Timed out) 600. ✓ 2.41 No 280 problem number 11 ✗ 25.391 ✗ 6.34 No 281 problem number 12 ✗ 25.373 ✗ 4.14 No 282 problem number 13 ✗ 30.129 ✗ 9.46 No 283 problem number 14 ✗ 1.546 ✓Solution contains RootOf 0.15 No 284 problem number 15 ✓ 0.413 ✓ 1.3 No 285 problem number 16 ✗ 88.877 ✗ 46.76 No 286 problem number 17 ✗ 144.362 ✓ 0.67 No 287 problem number 18 ✗ 86.632 ✓ 0.75 No 288 problem number 19 ✗ (Timed out) 600. ✓ 0.9 No 289 problem number 20 ✓ 0.054 ✓ 0.18 No 290 problem number 21 ✓ 0.389 ✓ 0.21 No 291 problem number 22 ✓ 0.224 ✓ 0.13 No 292 problem number 23 ✗ 26.614 ✓ 0.17 No 293 problem number 24 ✓ 0.122 ✓ 0.08 No 294 problem number 25 ✓ 0.318 ✓ 0.06 No 295 problem number 26 ✓ 0.499 ✓ 0.12 No 296 problem number 27 ✓ 0.094 ✓ 0.16 No 297 problem number 28 ✗ 0.105 ✓Solution contains RootOf 0.11 No 298 problem number 29 ✗ 0.114 ✓Solution contains RootOf 0.08 No 299 problem number 30 ✗ 0.392 ✓ 2.57 No 300 problem number 31 ✗ 22.68 ✓ 2.43 No 301 problem number 32 ✗ 145.72 ✗ 21.65 No 302 problem number 33 ✓ 0.075 ✓ 0.27 No 303 problem number 34 ✓ 0.025 ✓ 0.12 No 304 problem number 35 ✓ 0.051 ✓ 0.15 No 305 problem number 36 ✓ 0.167 ✓ 0.3 No 306 problem number 37 ✗ (Timed out) 600. ✓ 0.56 No 307 problem number 38 ✓ 1.329 ✓ 0.3 No 308 problem number 39 ✓ 0.08 ✓ 0.22 No 309 problem number 40 ✗ 140.148 ✗ 26.92 No 310 problem number 41 ✓ 0.141 ✓ 0.35 No 311 problem number 42 ✗ 3.373 ✓ 1.36 No 312 problem number 43 ✗ 2.53 ✓ 3.05 No 313 problem number 44 ✗ 141.42 ✗ 17.89 No 314 problem number 45 ✗ 141.973 ✗ 25.44 No 315 problem number 46 ✗ (Timed out) 600. ✓ 7.56 No 316 problem number 47 ✓ 40.931 ✓ 0.2 No 317 problem number 48 ✗ 35.988 ✓ 0.69 No 318 problem number 49 ✗ 24.009 ✗ 15.22 No 319 problem number 50 ✗ 112.817 ✗ 79.44 No 320 problem number 51 ✗ 0.143 ✓ 1.46 No 321 problem number 52 ✗ 9.488 ✗ 2.89 No 322 problem number 53 ✗ 0.262 ✓ 1.1 No 323 problem number 54 ✗ 0.171 ✗ 2.69 No 324 problem number 55 ✗ 26.003 ✗ 9.59 No 325 problem number 56 ✗ (Timed out) 422.926 ✓ 1.89 No 326 problem number 1 ✓ 0.011 ✓ 0.03 No 327 problem number 2 ✓ 0.016 ✓ 0.01 No 328 problem number 3 ✓ 0.081 ✓ 0.94 No 329 problem number 4 ✓ 0.128 ✓ 0.91 No 330 problem number 5 ✗ 22.988 ✓ 1.33 No 331 problem number 6 ✓ 0.029 ✓ 0.1 No 332 problem number 7 ✓ 0.096 ✓ 0.05 No 333 problem number 8 ✓ 0.152 ✓Has RootOf 1.59 No 334 problem number 9 ✓ 0.096 ✓ 0.34 No 335 problem number 10 ✗ 0.127 ✓ 1.84 No 336 problem number 11 ✗ 2.009 ✗ 3.34 No 337 problem number 1 ✓ 0.442 ✓ 0.57 No 338 problem number 2 ✓ 0.721 ✓ 0.3 No 339 problem number 3 ✓ 0.219 ✓ 0.09 No 340 problem number 4 ✗ 36.307 ✓ 0.26 No 341 problem number 5 ✓ 0.117 ✓ 0.13 No 342 problem number 6 ✗ 22.289 ✗ 8.44 No 343 problem number 7 ✓ 0.151 ✓ 0.19 No 344 problem number 8 ✗kernel error generated 0.451 ✓ 0.14 No 345 problem number 9 ✓ 0.809 ✓ 0.55 No 346 problem number 10 ✓ 0.772 ✓ 0.48 No 347 problem number 11 ✗ 21.587 ✓ 0.67 No 348 problem number 12 ✓ 1.637 ✓ 0.18 No 349 problem number 13 ✓ 0.058 ✓ 0.12 No 350 problem number 14 ✗ 23.167 ✗ 6.48 No 351 problem number 15 ✗ (Timed out) 600. ✓ 1.32 No 352 problem number 16 ✗ 22.107 ✗ 5.7 No 353 problem number 17 ✗ 222.07 ✓ 0.86 No 354 problem number 18 ✗ 22.419 ✗ 3.93 No 355 problem number 19 ✓ 0.103 ✓ 0.15 No 356 problem number 20 ✗ 22.246 ✗ 5.22 No 357 problem number 21 ✗ 23.949 ✗ 5.63 No 358 problem number 22 ✓ 1.745 ✓ 0.19 No 359 problem number 23 ✓ 0.113 ✓ 0.22 No 360 problem number 24 ✗ 21.324 ✗ 3.03 No 361 problem number 25 ✓ 0.133 ✓ 0.13 No 362 problem number 26 ✓ 0.157 ✓ 0.14 No 363 problem number 27 ✗ 0.609 ✓Solution contains RootOf 0.17 No 364 problem number 28 ✓ 6.496 ✓ 0.19 No 365 problem number 29 ✓ 0.08 ✓ 0.17 No 366 problem number 30 ✓ 2.582 ✓ 0.16 No 367 problem number 31 ✗ 46.99 ✓ 11.4 No 368 problem number 32 ✓ 0.046 ✓ 0.19 No 369 problem number 33 ✗ 0.081 ✓ 0.24 No 370 problem number 34 ✗ (Timed out) 600. ✓ 5.26 No 371 problem number 35 ✗ (Timed out) 600. ✓ 3.56 No 372 problem number 36 ✗ (Timed out) 600. ✓ 3.55 No 373 problem number 1 ✓ 0.014 ✓ 0.03 No 374 problem number 2 ✓ 0.048 ✓ 0.27 No 375 problem number 3 ✓ 59.26 ✓ 1.74 No 376 problem number 4 ✗ 42.041 ✓ 0.35 No 377 problem number 5 ✗ 54.596 ✓ 2.07 No 378 problem number 6 ✓ 0.183 ✓ 0.08 No 379 problem number 7 ✓ 0.022 ✓ 0.06 No 380 problem number 1 ✓ 0.011 ✓ 0.01 No 381 problem number 2 ✓ 0.032 ✓ 0.26 No 382 problem number 3 ✗ 58.088 ✓ 2.79 No 383 problem number 4 ✗ 58.999 ✓ 1.94 No 384 problem number 5 ✗ (Timed out) 600. ✓ 1.85 No 385 problem number 6 ✗ (Timed out) 600. ✓ 5.58 No 386 problem number 7 ✗ (Timed out) 600. ✓ 1.6 No 387 problem number 8 ✓ 0.038 ✓ 0.07 No 388 problem number 1 ✓ 0.021 ✓ 0.02 No 389 problem number 2 ✓ 0.03 ✓ 0. No 390 problem number 3 ✓ 2.305 ✓ 0.68 No 391 problem number 4 ✗ 42.71 ✓ 1.83 No 392 problem number 5 ✗ (Timed out) 600. ✓ 3.06 No 393 problem number 6 ✗ (Timed out) 600. ✓ 3.67 No 394 problem number 7 ✗ (Timed out) 600. ✓ 1.86 No 395 problem number 8 ✓ 285.009 ✓ 0.11 No 396 problem number 1 ✓ 0.021 ✓ 0.02 No 397 problem number 2 ✓ 0.032 ✓ 0.92 No 398 problem number 3 ✓ 2.063 ✓ 0.73 No 399 problem number 4 ✗ 3.979 ✓ 0.63 No 400 problem number 1 ✓ 0.065 ✓ 0.38 No 401 problem number 2 ✓ 0.169 ✓ 0.1 No 402 problem number 3 ✓ 1.754 ✓ 0.61 No 403 problem number 4 ✗ 13.368 ✓ 5.34 No 404 problem number 5 ✓ 0.035 ✓ 0.05 No 405 problem number 6 ✗ (Timed out) 600. ✓ 4.68 No 406 problem number 1 ✓ 0.033 ✓ 0.04 No 407 problem number 3 ✓ 574.234 ✓ 0.04 No 408 problem number 4 ✗ (Timed out) 600. ✓ 0.1 No 409 problem number 1 ✓ 0.066 ✓ 0.18 No 410 problem number 2 ✓ 0.077 ✓ 0.08 No 411 problem number 3 ✗ (Timed out) 600. ✓ 0.29 No 412 problem number 4 ✗ 21.998 ✓ 0.3 No 413 problem number 5 ✗ 22.667 ✗ 2.87 No 414 problem number 6 ✗ 26.276 ✓ 1.13 No 415 problem number 7 ✗ 26.528 ✗ 2.63 No 416 problem number 8 ✗ 23.434 ✗ 2.35 No 417 problem number 9 ✓ 0.211 ✓ 0.14 No 418 problem number 10 ✗ (Timed out) 600. ✓ 0.9 No 419 problem number 11 ✓ 0.068 ✓ 1.24 No 420 problem number 12 ✗ 20.674 ✗ 1.21 No 421 problem number 13 ✗ 22.797 ✗ 1.99 No 422 problem number 14 ✗ 21.9 ✗ 1.19 No 423 problem number 15 ✓ 0.15 ✓ 0.25 No 424 problem number 16 ✓ 0.057 ✓ 0.07 No 425 problem number 17 ✓ 0.657 ✓ 0.19 No 426 problem number 18 ✗ (Timed out) 600. ✓ 0.49 No 427 problem number 19 ✗ (Timed out) 600. ✓ 1.45 No 428 problem number 20 ✗ (Timed out) 600. ✓ 1.22 No 429 problem number 21 ✗ 26.047 ✓ 0.09 No 430 problem number 22 ✗ (Timed out) 600. ✓ 0.66 No 431 problem number 23 ✗ (Timed out) 600. ✓ 0.25 No 432 problem number 1 ✓ 0.23 ✓contains unresolved integral 0.44 No 433 problem number 2 ✓contains unresolved integral 395.282 ✓contains unresolved integral 0.69 No 434 problem number 3 ✓ 0.532 ✓contains unresolved integral 0.92 No 435 problem number 4 ✗ (Timed out) 600. ✓contains unresolved integral 1.27 No 436 problem number 5 ✗ 41.578 ✓ 2.06 No 437 problem number 6 ✗ 44.198 ✓contains unresolved integrals 0.22 No 438 problem number 7 ✗ 29.047 ✓contains unresolved integrals 3.92 No 439 problem number 8 ✗ 41.973 ✓ 0.39 No 440 problem number 9 ✗ 43.284 ✓ 4.68 No 441 problem number 10 ✗ 44.321 ✓ 1.75 No 442 problem number 11 ✗ (Timed out) 600. ✗ (Timed out) 600. No 443 problem number 12 ✗ (Timed out) 600. ✗ (Timed out) 600. No 444 problem number 13 ✓ 86.402 ✓ 0.26 No 445 problem number 14 ✗ (Timed out) 600. ✓ 1.23 No 446 problem number 1 ✓ 0.287 ✓Contains unresolved integral 0.2 No 447 problem number 2 ✓ 264.727 ✓ 0.32 No 448 problem number 3 ✓ 360.04 ✓ 1.4 No 449 problem number 4 ✗ (Timed out) 600. ✓ 0.55 No 450 problem number 5 ✗ 41.444 ✓ 0.47 No 451 problem number 6 ✗ 41.836 ✓ 0.35 No 452 problem number 7 ✗ 44.014 ✓ 0.84 No 453 problem number 8 ✗ 43.815 ✓ 0.84 No 454 problem number 9 ✗ (Timed out) 600. ✓ 1.99 No 455 problem number 10 ✗ (Timed out) 600. ✓ 3.11 No 456 problem number 11 ✗ (Timed out) 600. ✓ 6.04 No 457 problem number 12 ✗ (Timed out) 600. ✓ 2.44 No 458 problem number 1 ✓ 0.038 ✓ 0.01 No 459 problem number 2 ✓ 0.145 ✓ 0.14 No 460 problem number 3 ✓ 0.348 ✓Has unresolved integrals 0.46 No 461 problem number 4 ✗ 42.7 ✓ 0.38 No 462 problem number 5 ✗ 44.273 ✓ 0.38 No 463 problem number 6 ✗ (Timed out) 587.503 ✓ 0.64 No 464 problem number 7 ✗ 227.248 ✗ (Timed out) 600. No 465 problem number 8 ✗ 39.87 ✗ (Timed out) 600. No 466 problem number 9 ✗ (Timed out) 600. ✗ (Timed out) 600. No 467 problem number 10 ✓ 272.612 ✓ 0.2 No 468 problem number 11 ✗ (Timed out) 600. ✓ 11.42 No 469 problem number 12 ✗ 571.413 ✓ 2.01 No 470 problem number 13 ✗ (Timed out) 600. ✓ 1.69 No 471 problem number 14 ✗ (Timed out) 600. ✓ 3.3 No 472 problem number 15 ✗ (Timed out) 597.425 ✓ 1.99 No 473 problem number 1 ✓ 0.191 ✓Has unresolved integral 0.16 No 474 problem number 2 ✓ 350.865 ✓ 0.16 No 475 problem number 3 ✗ (Timed out) 600. ✓ 0.33 No 476 problem number 4 ✗ 42.78 ✓ 0.38 No 477 problem number 5 ✗ 44.481 ✓ 0.48 No 478 problem number 6 ✓ 0.289 ✓ 0.1 No 479 problem number 7 ✓ 0.136 ✓ 0.62 No 480 problem number 8 ✓ 0.116 ✓ 0.25 No 481 problem number 9 ✓ 0.821 ✓ 0.38 No 482 problem number 10 ✓ 1.303 ✓ 0.98 No 483 problem number 11 ✓ 0.114 ✓ 0.23 No 484 problem number 12 ✓ 600. ✓ 0.79 No 485 problem number 1 ✓ 0.657 ✓Has unresolved integrals 0.69 No 486 problem number 2 ✓ 1.025 ✓ 0.42 No 487 problem number 3 ✓ 0.562 ✓Mathematica answer is simpler 0.55 No 488 problem number 4 ✗ 24.048 ✗ (Timed out) 600. No 489 problem number 5 ✗ 42.472 ✓ 0.71 No 490 problem number 6 ✗ 60.923 ✓ 0.96 No 491 problem number 7 ✗ (Timed out) 600. ✗ (Timed out) 600. No 492 problem number 8 ✗ 24.592 ✓ 0.33 No 493 problem number 9 ✗ 23.545 ✓ 0. No 494 problem number 10 ✗ 39.682 ✓ 1.04 No 495 problem number 11 ✗ (Timed out) 600. ✗ 224.27 No 496 problem number 1 ✓ 0.096 ✓ 0.12 No 497 problem number 2 ✓ 600. ✓ 0.1 No 498 problem number 3 ✗ 274.513 ✓ 0.15 No 499 problem number 4 ✓ 0.236 ✓ 0.16 No 500 problem number 5 ✗ 210.37 ✓ 0.6 No 501 problem number 6 ✗ 22.494 ✓ 1.48 No 502 problem number 7 ✗ 26.791 ✓ 1.21 No 503 problem number 8 ✗ 225.976 ✓ 0.56 No 504 problem number 9 ✗ 275.922 ✗ 48.73 No 505 problem number 10 ✗ 35.736 ✗ 61.44 No 506 problem number 11 ✓ 600. ✓ 0.13 No 507 problem number 12 ✓ 62.942 ✓ 0.15 No 508 problem number 1 ✓ 0.092 ✓ 0.08 No 509 problem number 2 ✓ 600. ✓ 0.09 No 510 problem number 3 ✗ (Timed out) 600. ✓ 0.13 No 511 problem number 4 ✓ 0.198 ✓ 0.18 No 512 problem number 5 ✗ (Timed out) 600. ✓ 5.95 No 513 problem number 6 ✗ 28.905 ✗ 14.34 No 514 problem number 7 ✗ 257.267 ✓ 1.19 No 515 problem number 8 ✗ (Timed out) 600. ✓ 5.5 No 516 problem number 9 ✗ 250.715 ✗ 47.68 No 517 problem number 10 ✗ 36.64 ✗ 59.83 No 518 problem number 11 ✗ (Timed out) 600. ✓ 0.14 No 519 problem number 12 ✓ 60.138 ✓ 0.14 No 520 problem number 1 ✓ 600. ✓ 0.09 No 521 problem number 2 ✗ (Timed out) 600. ✓ 0.22 No 522 problem number 3 ✗ 600. ✓ 0.38 No 523 problem number 4 ✓ 600. ✓ 0.16 No 524 problem number 5 ✗ (Timed out) 600. ✓ 0.77 No 525 problem number 6 ✗ 521.971 ✓ 0.48 No 526 problem number 7 ✗ (Timed out) 600. ✓ 1.18 No 527 problem number 8 ✗ (Timed out) 600. ✓ 0.04 No 528 problem number 9 ✗ (Timed out) 600. ✗ 10.79 No 529 problem number 10 ✗ 39.072 ✗ 515.11 No 530 problem number 11 ✗ (Timed out) 600. ✓ 0.11 No 531 problem number 12 ✗ (Timed out) 600. ✓ 0.2 No 532 problem number 1 ✗ (Timed out) 600. ✓ 0.12 No 533 problem number 2 ✗ (Timed out) 600. ✓ 0.1 No 534 problem number 3 ✗ 512.078 ✓ 0.2 No 535 problem number 4 ✗ (Timed out) 600. ✓ 0.19 No 536 problem number 5 ✗ (Timed out) 600. ✓ 1.54 No 537 problem number 6 ✗ (Timed out) 600. ✓ 0.42 No 538 problem number 7 ✗ (Timed out) 600. ✓ 1.51 No 539 problem number 8 ✗ 33.739 ✗ 6.32 No 540 problem number 9 ✗ (Timed out) 600. ✗ 22.72 No 541 problem number 10 ✗ 40.222 ✗ 379.21 No 542 problem number 11 ✗ (Timed out) 600. ✓ 0.14 No 543 problem number 12 ✗ (Timed out) 600. ✓ 0.36 No 544 problem number 1 ✓ 0.633 ✓ 0.03 No 545 problem number 2 ✓ 0.996 ✓ 0.09 No 546 problem number 3 ✗ 113.787 ✓ 0.07 No 547 problem number 4 ✗ 20.499 ✓ 0.07 No 548 problem number 5 ✗ 24.329 ✓ 0.48 No 549 problem number 6 ✗ 134.698 ✓ 0.07 No 550 problem number 7 ✗ 23.579 ✗ 2.51 No 551 problem number 8 ✗ 23.518 ✗ 2.85 No 552 problem number 9 ✗ 39.825 ✓ 0.08 No 553 problem number 10 ✗ 28.007 ✗ 8.13 No