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= dt 3. The differential equation describing the variation of capacitor charge in d²q dq an alternating current circuit is given by +2 = 2q = dt² 50 cos 2t. Find an expression for the charge q of the capacitor in the dq circuit at any time t seconds, given that t = 0, q = 0 and = 0 4. Show that y = -2x + 3 is a particular integral of the differential equation 23 d9y = 18x + 19. Hence find the general solution of the 12d²y dx² dx differential equation. 5. Solve the differential equation v = x + y + 4. dy dx = (x + y + 4)², using the substitution

= dt 3. The differential equation describing the variation of capacitor charge in d²q dq an alternating current circuit is given by +2 = 2q = dt² 50 cos 2t. Find an expression for the charge q of the capacitor in the dq circuit at any time t seconds, given that t = 0, q = 0 and = 0 4. Show that y = -2x + 3 is a particular integral of the differential equation 23 d9y = 18x + 19. Hence find the general solution of the 12d²y dx² dx differential equation. 5. Solve the differential equation v = x + y + 4. dy dx = (x + y + 4)², using the substitution

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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dt 3. The differential equation describing the variation of capacitor charge in d²q dq an alternating current circuit is given by +2: = = 2q = dt² 50 cos 2t. Find an expression for the charge q of the capacitor in the circuit at any time t seconds, given that t = 0, q = 0 and dq dt 12 - d²y 4. Show that y = -2x + 3 is a particular integral of the differential equation - 9y = 18x + 19. Hence find the general solution of the differential equation. dy dx² dx 23 0 dy 5. Solve the differential equation dx = (x + y + 4)², using the substitution dx v = x + y + 4.
Transcribed Image Text:dt 3. The differential equation describing the variation of capacitor charge in d²q dq an alternating current circuit is given by +2: = = 2q = dt² 50 cos 2t. Find an expression for the charge q of the capacitor in the circuit at any time t seconds, given that t = 0, q = 0 and dq dt 12 - d²y 4. Show that y = -2x + 3 is a particular integral of the differential equation - 9y = 18x + 19. Hence find the general solution of the differential equation. dy dx² dx 23 0 dy 5. Solve the differential equation dx = (x + y + 4)², using the substitution dx v = x + y + 4.
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