End-of-chapter review exercise 24 · 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

First-order linear differential equations — objective 1

Maths4U Original · Short practice

Solve \(y'+3y=13e^{4x},\ y(0)=14\). Write the solution as \(y=Ce^{-3x}+Ke^{4x}\).

Find K.

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

Fresh review variant

First-order linear differential equations — objective 1

Maths4U Original · Short practice

Solve \(y'+1y=14e^{1x},\ y(0)=15\). Write the solution as \(y=Ce^{-1x}+Ke^{1x}\).

Find K.

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

Method

First-order linear differential equations — objective 2

Maths4U Original · Short practice

Solve \(y'+1y=14e^{1x},\ y(0)=15\). Write the solution as \(y=Ce^{-1x}+Ke^{1x}\).

Find C.

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

Fresh review variant

First-order linear differential equations — objective 2

Maths4U Original · Short practice

Solve \(y'+2y=15e^{2x},\ y(0)=16\). Write the solution as \(y=Ce^{-2x}+Ke^{2x}\).

Find C.

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

Apply

Inhomogeneous equations and resonance — objective 3

Maths4U Original · Short practice

\(y''+6y'+8y=16e^{-2x},\ y(0)=14,\ y'(0)=15\). Write \(y=(A+Px)e^{-2x}+Be^{-4x}\).

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

Inhomogeneous equations and resonance — objective 3

Maths4U Original · Short practice

\(y''+8y'+15y=17e^{-3x},\ y(0)=15,\ y'(0)=16\). Write \(y=(A+Px)e^{-3x}+Be^{-5x}\).

Find B.

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

Check understanding

Substitution methods for differential equations — objective 4

Maths4U Original · Short practice

\(\displaystyle y'+3y=16y^2,\ y(0)=\frac{1}{18}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{3x}+ \frac{16}{3}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).

Find y′(0).

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

Fresh review variant

Substitution methods for differential equations — objective 4

Maths4U Original · Short practice

\(\displaystyle y'+1y=17y^2,\ y(0)=\frac{1}{19}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{1x}+ \frac{17}{1}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).

Find y′(0).

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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