Example 7 - Chapter 9 Class 12 Differential Equations
Last updated at July 14, 2026 by Teachoo
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Example 1 (i)
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Chapter 9 Class 12 Differential Equations
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Example 7 Find the equation of the curve passing through the point (1 , 1) whose differential equation is š„ šš¦= (2š„^2+1)šš„(š„ā 0) š„ šš¦ = (2x2 + 1)dx dy = "(2x2 + 1)" /š„ dx dy = ("2x2" /š„+1/š„) dx dy = (šš+š/š) dx Integrating both sides. ā«1āšš¦ = ā«1ā(2š„+1/š„) šš„ ā«1āšš¦ = ā«1āć2š„ šš„+ć ā«1āć1/š„ šš„ć y = 2 š„2/2 + log |š„| + C y = šš + log |š| + C Since the curve passes through point (1, 1) Putting x = 1, y = 1 is (1) 1 = 12 + log |š| + C 1 = 1 + 0 + C 1 ā 1 = C ā“ C = 0 Put C = 0 in (1) y = x2 + log |š„| + C y = x2 + log |š| + 0 y = x2 + log |š„| Hence, the equation of curve is y = x2 + log |š|
