// Numbas version: exam_results_page_options
{"name": "Maria's copy of Solve a separable first order ODE,", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"type": "question", "parts": [{"scripts": {}, "type": "gapfill", "gaps": [{"checkingtype": "absdiff", "type": "jme", "answersimplification": "all", "showCorrectAnswer": true, "vsetrangepoints": 5, "expectedvariablenames": [], "vsetrange": [0, 1], "checkingaccuracy": 0.001, "scripts": {}, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": ["."], "message": "<p>Do not enter decimals in your answer.</p>"}, "marks": 1, "showpreview": true, "answer": "{(d1*a1-b1*c1)}/{a1+c1}+{(d1+b1)}*x/{a1+c1}", "checkvariablenames": false}], "showCorrectAnswer": true, "marks": 0, "prompt": "<p>$y=$ [[0]] (Do not enter decimals in your answer.)</p>"}], "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "functions": {}, "tags": ["checked2015", "MAS1603", "MAS2105"], "advice": "<p>The differential equation is separable, so we can write</p>\n<p>\\[\\int{\\!\\frac{1}{\\var{b1}+y}\\,\\mathrm{d}y} = \\int{\\!\\frac{1}{\\var{a1}+x}\\,\\mathrm{d}x},\\]</p>\n<p>then</p>\n<p>\\[\\ln\\lvert\\var{b1}+y\\rvert=\\ln\\lvert\\var{a1}+x\\rvert+c,\\]</p>\n<p>so</p>\n<p>\\[y=\\simplify{A({a1}+x)-{b1}},\\]</p>\n<p>which is the general solution of the equation.</p>\n<p>Now,</p>\n<p>\\[\\var{d1}=y(\\var{c1})=\\simplify[std]{A({a1}+{c1})-{b1}},\\]</p>\n<p>so</p>\n<p>\\[A=\\simplify[std]{({d1}+{b1})/({a1}+{c1})}=\\simplify{{d1+b1}/{a1+c1}},\\]</p>\n<p>and then the full solution is</p>\n<p>\\[y=\\simplify[std]{{d1+b1}/{a1+c1}({a1}+x)-{b1}}=\\simplify{{(d1*a1-b1*c1)}/{a1+c1}+{(d1+b1)}*x/{a1+c1}}.\\]</p>", "showQuestionGroupNames": false, "name": "Maria's copy of Solve a separable first order ODE,", "statement": "<p>Find the solution of the differential equation</p>\n  <p>\\[(\\var{a1}+x)y'=\\var{b1}+y,\\]</p>\n  <p>satisfying $y(\\var{c1})=\\var{d1}$.</p>", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Find the solution of a first order separable differential equation of the form $(a+x)y'=b+y$.</p>"}, "preamble": {"css": "", "js": ""}, "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "variable_groups": [], "ungrouped_variables": ["a1", "c1", "b1", "d1"], "variables": {"a1": {"name": "a1", "definition": "random(1..9)*sign(random(-1,1))", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "b1": {"name": "b1", "definition": "random(1..9)*sign(random(-1,1))", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "d1": {"name": "d1", "definition": "random(1..9 except abs(b1))*sign(random(-1,1))", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "c1": {"name": "c1", "definition": "random(1..9 except abs(a1))*sign(random(-1,1))", "templateType": "anything", "description": "", "group": "Ungrouped variables"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}