Question:
The general solution of the differential equation 4xy+12x+(2x2+3)y' = 0 is
The general solution of the differential equation 4xy+12x+(2x2+3)y' = 0 is
Updated On: Apr 4, 2025
- \(\frac{2x^2+3}{y+3}=C\)
- \(\frac{y-3}{2x^2+3}=C\)
- \(\frac{y+2}{2x^2+3}=C\)
- (y-3)(2x2+3)=C
- (y+3)(2x2+3)=C
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The Correct Option is
Solution and Explanation
The given differential equation is \( 4xy + 12x + (2x^2 + 3)y' = 0 \).
First, we can rewrite the equation in a more standard form:
\( y' = -\frac{4xy + 12x}{2x^2 + 3} \).
This is a linear first-order differential equation. We can try separating the variables or use an appropriate substitution. After simplifying and solving the equation, we obtain the general solution:
\( (y + 3)(2x^2 + 3) = C \),
where \( C \) is the constant of integration.
The correct answer is \( (y + 3)(2x^2 + 3) = C \).
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