Second order differential equations: The homogeneous case · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Second-order homogeneous equations — objective 1

Maths4U Original · Short practice

\(y''+3y'+2y=0,\ y(0)=14,\ y'(0)=15\). Write \(y=Ae^{-1x}+Be^{-2x}\).

Find A.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Second-order homogeneous equations — objective 1

Maths4U Original · Short practice

\(y''+6y'+8y=0,\ y(0)=15,\ y'(0)=16\). Write \(y=Ae^{-2x}+Be^{-4x}\).

Find A.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Second-order homogeneous equations — objective 2

Maths4U Original · Short practice

\(y''+6y'+8y=0,\ y(0)=15,\ y'(0)=16\). Write \(y=Ae^{-2x}+Be^{-4x}\).

Find B.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Second-order homogeneous equations — objective 2

Maths4U Original · Short practice

\(y''+9y'+18y=0,\ y(0)=16,\ y'(0)=17\). Write \(y=Ae^{-3x}+Be^{-6x}\).

Find B.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Complex auxiliary roots — objective 3

Maths4U Original · Short practice

\(y''+6y'+25y=0,\ y(0)=16,\ y'(0)=17\). Use \(y=e^{-3x}(C\cos 4x+D\sin 4x)\).

Find the undamped trigonometric period.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Complex auxiliary roots — objective 3

Maths4U Original · Short practice

\(y''+2y'+26y=0,\ y(0)=17,\ y'(0)=18\). Use \(y=e^{-1x}(C\cos 5x+D\sin 5x)\).

Find the undamped trigonometric period.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Complex auxiliary roots — objective 4

Maths4U Original · Short practice

\(y''+2y'+26y=0,\ y(0)=17,\ y'(0)=18\). Use \(y=e^{-1x}(C\cos 5x+D\sin 5x)\).

Find y at \(\displaystyle x= \frac{\pi }{b}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Complex auxiliary roots — objective 4

Maths4U Original · Short practice

\(y''+4y'+8y=0,\ y(0)=18,\ y'(0)=19\). Use \(y=e^{-2x}(C\cos 2x+D\sin 2x)\).

Find y at \(\displaystyle x= \frac{\pi }{b}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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