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CBSE Class 12 Mathematics 2026 Main Paper 65/4/3 · Q161 Markslinear_differential_equations

CBSE Class 12 Mathematics 2026 Main Paper 65/4/3 · Question 16 (Differential Equations)

Which equation cannot be written as a first-order linear equation in one variable as a function of the other by isolating its derivative?

(A) (1+x²)dy+2xy dx=cot x dx
(B) y+d(xy)/dx=x(sin x+ln x)
(C) x(1+y²)dx−y(1+x²)dy=0
(D) y dx−(x+3y²)dy=0

✅ Step-by-Step Solution

Final Answer: x(1+y²)dx−y(1+x²)dy=0

A and B are linear in y(x), and D is linear in x(y) after division by y. In C either orientation leaves the dependent variable in a nonlinear rational expression.

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