// Numbas version: finer_feedback_settings
{"name": "General solution to 2nd order PDE: student can pick names of the arbitrary functions.", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "General solution to 2nd order PDE: student can pick names of the arbitrary functions.", "tags": [], "metadata": {"description": "<p>The student has to write the general solution of a 2nd order PDE. They can choose the names of their arbitrary functions of $x$ and $y$.</p>\n<p>The marking algorithm finds the names of the functions of $x$ and $y$ in the student's answer, and replaces them with $\\sin(x)$ and $\\cos(y)$ (these could be changed) so that the expression can be evaluated.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>\\[ u_{xy} = \\simplify{{a}x + {b}y} \\]</p>", "advice": "<p>For arbitrary functions $F$ and $G$, the general solution is:</p>\n<p>\\[ u(x,y) = \\simplify{ {a}*x^2y/2 + {b}x*y^2/2 + F(x) + G(x) \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a,b": {"name": "a,b", "group": "Ungrouped variables", "definition": "repeat(random(2..10),2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a,b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "fn_x (The name of the arbitrary function of x): match(studentExpr, \"m_anywhere(m_func(?;fn,[x]))\")[\"groups\"][\"fn\"] |> eval()\n\nfn_y (The name of the arbitrary function of y): match(studentExpr, \"m_anywhere(m_func(?;fn,[y]))\")[\"groups\"][\"fn\"] |> eval()\n\nfixed_fn_x: \"sin(x)\"\n\nfixed_fn_y: \"cos(y)\"\n\nstudentCompare: replace(\"{fn_x}(x)\", fixed_fn_x, replace(\"{fn_y}(y)\", fixed_fn_y, studentExpr))\n\ncorrectCompare: replace(\"F(x)\", \"sin(x)\", replace(\"G(y)\", fixed_fn_y, correctExpr))\n\nvalue_generators (Expressions which generate values for each variable in the answer):\n  [\"x\": default_value_generator[\"number\"],\n   \"y\": default_value_generator[\"number\"]\n  ]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Write the general solution $u(x,y)$.</p>", "answer": "{a}*x^2y/2 + {b}*x*y^2/2 + F(x)+G(y)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "f", "value": ""}, {"name": "g", "value": ""}, {"name": "x", "value": ""}, {"name": "y", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Shweta Sharma", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21418/"}], "resources": []}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Shweta Sharma", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21418/"}]}