Grouping exact differentials such as d(xy) or d(y/x)
This type of question, asked 2 times: 11 Apr 2023, 8 Apr 2024. All 2 questions below, oldest first.
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Question 1
11 Apr 2023
75
Let y=y(x) be a solution curve of the differential equation, (1−x2y2)dx=ydx+xdy. If the line x=1 intersects the curve y=y(x) at y=2 and the line x=2 intersects the curve y=y(x) at y=α, then a value of α is
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Question 2
8 Apr 2024
179
Let α∣x∣=∣y∣exy−β,α,β∈N be the solution of the differential equation xdy−ydx+xy(xdy+ydx)=0, y(1)=2. Then α+β is equal to
