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Elementary Differential Equation
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What is the standard structural form of a first-order linear ordinary differential equation?
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For the first-order linear differential equation x²(dy/dx) − 3y = √x, what is the integrating factor μ(x) after converting to standard form?
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What is the vital mathematical consistency condition (exactness test) required for a differential equation to be classified as exact?
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Upon substituting z = y^(1−n), a Bernoulli equation is transformed into which of the following standard linear differential equations?
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If the auxiliary equation am² + bm + c = 0 yields two distinct real roots m₁ and m₂ (Case I), what is the correct form of the general solution?
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8. Why is d²y/dx² + y(dy/dx) = 0 classified as non-linear?
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10. The ODE derived from y = Ae⁻⁴ˣ + Be⁻⁶ˣ is:
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11. If y = Ae³ˣ + Be⁻²ˣ has two arbitrary constants, how many times must it be differentiated to form the ODE?
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1. A differential equation is best defined as:
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4. What is the ORDER of the differential equation: 4(d³y/dx³) + sin x (d²y/dx²) + 5xy = 0?
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