1. Solve the ODE. (e2y-ycos(xy))dx + (2xe²y - x cos(xy) +2y)dy = 0 2. Solve the IVP. y" + y = g(t) y(0) = 0, y' (0) = 1 - {; t 0 1 } 3. 4. g(t) = Write the general solution of the ODE by finding two power series solutions about the ordinary point x = 0. Write out the first 3 nonzero terms in each series. (x²+1)y" + xy-y=0 Find the charge on the capacitor in an LRC-series circuit if L = 1 henry, R = 4 ohms, C=0.2 farad, and E(t) = 120 volts. The initial charge and the initial current are both zero. 5. Solve the ODE. dy (2x-3)(21) y = dx 6. 2(x-2)(x-1) Find the general solution of the ODE. y"-6y' +9y=x-33x 7. Find the general solution of the ODE on (0,00). 8. x²y" - xy' + y = 2x Solve the IVP. Answer in explicit form. State the interval of validity for your solution. dy dx x(x+1)- +xy = 1 y(e) = 1 Find the general solution of the ODE. 9. y" + 4y = 3 sin(2x)

1. Solve the ODE. (e2y-ycos(xy))dx + (2xe²y - x cos(xy) +2y)dy = 0 2. Solve the IVP. y" + y = g(t) y(0) = 0, y' (0) = 1 - {; t 0 1 } 3. 4. g(t) = Write the general solution of the ODE by finding two power series solutions about the ordinary point x = 0. Write out the first 3 nonzero terms in each series. (x²+1)y" + xy-y=0 Find the charge on the capacitor in an LRC-series circuit if L = 1 henry, R = 4 ohms, C=0.2 farad, and E(t) = 120 volts. The initial charge and the initial current are both zero. 5. Solve the ODE. dy (2x-3)(21) y = dx 6. 2(x-2)(x-1) Find the general solution of the ODE. y"-6y' +9y=x-33x 7. Find the general solution of the ODE on (0,00). 8. x²y" - xy' + y = 2x Solve the IVP. Answer in explicit form. State the interval of validity for your solution. dy dx x(x+1)- +xy = 1 y(e) = 1 Find the general solution of the ODE. 9. y" + 4y = 3 sin(2x)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

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