(Solved): please help me solve problem #4 and wxplain step by step,thank you In Problems 1-8, find a general s ...

In Problems 1-8, find a general solution to the differential equation using the method of variation of parameters. 14. $$y^{?}(?)+y(?)={\sec }^3?$$ 1. $$y^{??}+4y=\tan 2t$$ 15. $$y^{??}+y=3\sec t?t^2+1$$ 2. $$y^{??}+y=\sec i$$ 16. $$y^{??}+5y^{?}+6y=18t^2$$ 3. $$y^{??}?2y^{?}+y=i^{?1}{e}^{?}$$ 17. $$\frac{1}{2}{y}^{?}+2y=\tan 2t?\frac{1}{2}{e}^t$$ 4. $$y^{??}+2y^{?}+y=e^{?1}$$ 18. $$y^{??}?6y^{?}+9y=t^{?3}{e}^{34}$$ 5. $$y^{??}(?)+16y(?)=\sec 4?$$ 6. $$y^{??}+9y={\sec }^2(3t)$$ 19. Express the solution to the initial value problem 7. $$y^{??}+4y^{?}+4y=e^{?2t}\ln t$$ 8. $$y^{??}+4y={\csc }^2(2t)$$ $$y^{??}?y=\frac{1}{t},y(1)=0,y^{?}(1)=?2$$. using definite integrals. Using numerical integration In Problems 9 and 10, find a particular solution first by unde(Appendix C) to approximate the integrals, find an temined coefficients, and then by variation of parameters. approximation for $$y(2)$$ to two decimal places. Which method was quicker? 20. Use the method of variation of parameters to show that 9. $$y^{??}?y=2t+4$$ 10. $$2x^{??}(t)?2x^{?}(t)?4x(t)=2e^{2t}$$ $$y(t)=c_1\cos t+c_2\sin t+{?}_0^{t}f(s)\sin (t?s)ds$$ In Problems $$11?18$$, find a general solution to the differential is a general solution to the differential equation equation. $$y^{??}+y=f(t)$$ 11. $$y^{??}+y=\tan t+e^{3t}?1$$ where $$f(t)$$ is a continuous function on $$(??,?)$$. 12. $$y^{??}+y={\tan }^{2}t$$ [Hint: Use the trigonometric identity $$\sin (t?s)=$$ 13. $$v^{?}+4v={\sec }^4(2t)$$ $$\sin t\cos s?\sin s\cos t]$$