Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at May 29, 2023 by Teachoo

Example 7 Find the equation of the curve passing through the point (1 , 1) whose differential equation is π₯ ππ¦= (2π₯^2+1)ππ₯(π₯β 0) π₯ ππ¦ = (2x2 + 1)dx dy = "(2x2 + 1)" /π₯ dx dy = ("2x2" /π₯+1/π₯) dx dy = (2π₯+1/π₯) dx Integrating both sides. β«1βππ¦ = β«1β(2π₯+1/π₯) ππ₯ β«1βππ¦ = β«1βγ2π₯ ππ₯+γ β«1βγ1/π₯ ππ₯γ y = 2 π₯2/2 + log |π₯| + C y = π₯2 + log |π₯| + C Since the curve passes through point (1, 1) Putting x = 1, y = 1 is (1) 1 = 12 + log |π| + C 1 = 1 + 0 + C 1 β 1 = C β΄ C = 0 Put C = 0 in (1) i.e y = x2 + log |π₯| + C y = x2 + log |π₯| + 0 y = x2 + log |π₯| Hence, the equation of curve is y = x2 + log |π|