Question:
Differential equation for family \(y=ae^{2x}+bx^2\) is
Differential equation for family \(y=ae^{2x}+bx^2\) is
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To eliminate parameters, always differentiate twice.
Updated On: Jun 22, 2026
- \((1-2x^2)\frac{dy}{dx}\)
- \((2-4x^2)\frac{dy}{dx}\)
- \((1-2x)\frac{dy}{dx}\)
- \((2-4x)\frac{dy}{dx}\) \bigskip
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The Correct Option is D
Solution and Explanation
Concept:
Eliminate parameters \(a,b\).
Step 1: Differentiate.
\[ y'=2ae^{2x}+2bx \] \[ y''=4ae^{2x}+2b \]
Step 2: Eliminate constants.
Solve for \(a,b\) and substitute.
Step 3: Final equation.
\[ (x-x^2)y''+(2-4x)y' = 0 \] \[ \boxed{(D)} \]
Step 1: Differentiate.
\[ y'=2ae^{2x}+2bx \] \[ y''=4ae^{2x}+2b \]
Step 2: Eliminate constants.
Solve for \(a,b\) and substitute.
Step 3: Final equation.
\[ (x-x^2)y''+(2-4x)y' = 0 \] \[ \boxed{(D)} \]
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