st","extracted_subject":"MATH","extracted_chapter":"DIFFERENTIAL EQUATIONS","extracted_topic":"ORDER AND DEGREE OF DIFFERENTIAL EQUATIONS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1745.png?top_left_x=0&top_left_y=1515&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e70425d76b7ab31d210","slug":"the-order-of-the-differential-equation-of-all-tang-1","content":"The order of the differential equation of all tangent lines to the parabola y = x² is","options":[{"_id":"68a44cb77f15af4716cbb282","text":"1","sequence":0,"isCorrect":true},{"_id":"68a44cb77f15af4716cbb283","text":"2","sequence":1,"isCorrect":false},{"_id":"68a44cb77f15af4716cbb284","text":"3","sequence":2,"isCorrect":false},{"_id":"68a44cb77f15af4716cbb285","text":"4","sequence":3,"isCorrect":false}],"correct_answer":"1","explanation":"The parametric form of the given equation is x = t, y = t². The equation of any tangent at\n\nt is 2xt = y + t². Differentiating, we get 2t = y₁. Putting this value in the equation of tangent, we have 2 x y₁/2 = y + (y₁/2)² ̃ 4xy₁ = 4y + y₁²\n\nThe order of this equation is one.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:36.432Z","__v":0,"vector_store_id":"26c84e37-8ca9-4ba1-9a07-d585f96b2ef7","updated_at":"2024-08-30T21:49:36.432Z","isStarred":false},"params":{"questionSlug":"the-order-of-the-differential-equation-of-all-tang-1"}}]}]]

Question: The order of the differential equation of all tangent lines to the parabola y = x<sup>2</sup> is...

Solution