MATH142 (DB125) Essentials of Engineering Mathematics

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Solve the differential equation.

3x²y' - 2xy = y^-3

y² = + Cx^8/3

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y² = + Cx^11/3

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y⁴ = + Cx^11/3

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y⁴ = + Cx^8/3

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Solve the differential equation.

-x³y' + 2x²y = y²

y =

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y =

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y =

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y =

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Solve the differential equation subject to the initial condition.

x + (1 + x)y = 1; y(5) = 2

y =

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y =

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y =

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y =

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Solve the differential equation subject to the initial condition.

+ 10xy - e^-5x2 = 0; y(0) = 4

y = xe^-5x2 + 4

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y = (x + 4)e^-5x2

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y = xe^-5x + 4

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y = (x + 4)e^-5x

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Find the particular solution for the initial value problem.

x = 4x²e2x; y(0) = 16

y = 4xe2x - 2e2x + 18

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y = 2xe2x - e2x + 17

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y = 2xe2x + 16

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y = 4xe2x - e2x + 17

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Find the particular solution for the initial value problem.

(4x + 4)y = ; y(0) = 1

y = e^{4x2 + 4x} + 1

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y = e^{2x2 + 4x}

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y = e^{4x2 + 4x}

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y = e^{2x2 + 4x + 1}

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Find the general solution for the differential equation.

= y²(4 - e^x)

y =

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y = 4x - e^x + C

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y =

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y =

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