A family of solution curves y = Cx² and one particular solutionहल वक्रों का कुल y = Cx² और एक विशिष्ट हलSolution curves ki family y = Cx² aur ek particular solution

NCERT 9.3 · Class 12 Maths · Chapter 9 · interactive diagram

Parts and what they mean

• The differential equation x\,\frac{dy}{dx} = 2y (अवकल समीकरण x\,\frac{dy}{dx} = 2y) — Check: y = Cx^2 \Rightarrow y' = 2Cx \Rightarrow x y' = 2Cx^2 = 2y. So every curve in the picture is a solution.
• General solution y = Cx^2 (grey curves) (व्यापक हल y = Cx^2 (धूसर वक्र)) — One arbitrary constant C gives a whole family: one curve for every value of C.
• C = 0: the line y = 0 (C = 0: रेखा y = 0) — Also a member of the family (y = 0 satisfies xy' = 2y).
• Particular solution y = 2x^2 (विशिष्ट हल y = 2x^2) — Put x = 1, y = 2 in y = Cx^2: 2 = C. No arbitrary constant is left.
• Given point (1, 2) (दिया हुआ बिंदु (1, 2)) — The condition "the curve passes through (1, 2)" picks exactly one curve from the family.
• x-axis (x-अक्ष) — The horizontal number line; inputs x are read here.
• y-axis (y-अक्ष) — The vertical number line; outputs y = f(x) are read here.
• Origin O(0, 0) (मूल बिंदु O(0, 0)) — Where the two axes cross.

Original diagram drawn by Simple Learning Hub, based on NCERT 9.3. Report a mistake