End-of-chapter review exercise 24: check 1
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 24: review variant 1
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 24: check 2
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 24: review variant 2
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 24: check 3
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 24: review variant 3
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 24: check 4
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 24: review variant 4
Difficulty: ★★☆Info
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.