Mathematics · Differential Equations

अवकल समीकरण y'' + 4y' + 4y = 0 के स्वतंत्र हलों (independent solutions) का समुच्चय है:

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1{e-3x, e-x}
2{e-2x, e2x}
3{e2x, xe2x}
4{e-2x, xe-2x}✓

सही उत्तर देखें

{e-2x, xe-2x}

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For a ∈ ℝ, let y1(x) and y2(x) be solutions of the differential equation: y'' + (ex2 + cos x)y = 0 such that y1(0) = 3, y1'(0) = -1, y2(0) = -5, y2'(0) = a. Suppose W(y1, y2)(x) denotes the Wronskian of y1 and y2. If W(y1, y2)12 = 4, then the value of a is:

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The integrating factor for the linear differential equation (1 + x2)dydx + 2xy = cot(x) is:

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अवकल समीकरण y'' + 4y' + 4y = 0 के स्वतंत्र हलों (independent solutions) का समुच्चय है:

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अवकल समीकरण y'' + 4y' + 4y = 0 के स्वतंत्र हलों (independent solutions) का समुच्चय है:

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