Second order differential equations: The homogeneous case: check 1
Difficulty: ★★☆Info
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.
Second order differential equations: The homogeneous case: review variant 1
Difficulty: ★★☆Info
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.
Second order differential equations: The homogeneous case: check 2
Difficulty: ★★☆Info
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.
Second order differential equations: The homogeneous case: review variant 2
Difficulty: ★★☆Info
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.
Second order differential equations: The homogeneous case: check 3
Difficulty: ★★☆Info
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.
Second order differential equations: The homogeneous case: review variant 3
Difficulty: ★★☆Info
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.
Second order differential equations: The homogeneous case: check 4
Difficulty: ★★☆Info
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.
Second order differential equations: The homogeneous case: review variant 4
Difficulty: ★★☆Info
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.