Example 8 - Chapter 9 Class 12 Differential Equations
Last updated at July 14, 2026 by Teachoo
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Chapter 9 Class 12 Differential Equations
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Example 8 Find the equation of a curve passing through the point (ā2 ,3), given that the slope of the tangent to the curve at any point (š„ , š¦) is 2š„/š¦^2 Slope of tangent = šš¦/šš„ ā“ š š/š š = šš/šš š¦2 dy = 2x dx Integrating both sides ā«1āšš š š= ā«1āćšš š šć š¦^3/3 = 2.š„^2/2 + C š¦^3/3 = š„^2 + C š¦^3 = ć3š„ć^2+3š¶ š^š = ćššć^š+šŖš where š¶1 = 3C Given that equation passes through (ā2, 3) Putting x = ā2, y = 3 in (1) y3 = 3x2 + C1 33 = 3(ā2)2 + C1 27 = 3 Ć 4 + C1 27 ā 12 = C1 15 = C1 C1 = 15 Putting C1 in (1) y3 = 3x2 + 15 y = "(3x2 + " ć"15)" ć^(š/š) " "is the particular solution of the equation.
