1. \(y_{p}=-1+2x+3x^{2};\: y=-1+2x+3x^{2}+c_{1}e^{-6x}+c_{2}e^{x}\)
2. \(y_{p}=1+x;\: y=1+x+e^{2x}(c_{1}\cos x+c_{2}\sin x)\)
3. \(y_{p}=-x+x^{3};\: y=-x+x^{3}+c_{1}e^{-7x}+c_{2}e^{-x}\)
4. \(y_{p} = 1 − x^{2};\: y = 1 − x^{2} + e^{2x} (c_{1} + c_{2}x)\)
5. \(y_{p} = 2x + x^{3};\: y = 2x + x^{3} + e^{−x} (c_{1} \cos 3x + c_{2} \sin 3x);\: y = 2x + x^{3} + e^{−x} (2 \cos 3x + 3 \sin 3x)\)
6. \(y_{p} = 1 + 2x;\: y = 1 + 2x + e^{−3x} (c_{1} \cos x + c_{2} \sin x);\: y = 1 + 2x + e^{−3x} (\cos x − \sin x)\)
8. \(y_{p}=\frac{2}{x}\)
9. \(y_{p}=4x^{1/2}\)
10. \(y_{p}=\frac{x^{3}}{2}\)
11. \(y_{p}=\frac{1}{x^{3}}\)
12. \(y_{p}=9x^{1/3}\)
13. \(y_{p}=\frac{2x^{4}}{13}\)
16. \(y_{p}=\frac{e^{3x}}{3};\: y=\frac{e^{3x}}{3}+c_{1}e^{-6x}+c_{2}e^{x}\)
17. \(y_{p} = e^{2x};\: y = e^{2x} (1 + c_{1}\cos x + c_{2}\sin x)\)
18. \(y = −2e^{−2x};\: y = −2e^{−2x} + c_{1}e^{−7x} + c_{2}e^{−x};\: y = −2e^{−2x} − e^{−7x} + e^{−x}\)
19. \(y_{p} = e^{x};\: y = e^{x} + e^{2x} (c_{1} + c_{2}x);\: y = e^{x} + e^{2x} (1 − 3x)\)
20. \(y_{p}=\frac{4}{25}e^{x/2};\: y=\frac{4}{45}e^{x/2}+e^{-x}(c_{1}\cos 3x+c_{2}\sin 3x)\)
21. \(y_{p} = e^{−3x};\: y = e^{−3x} (1 + c_{1}\cos x + c_{2}\sin x)\)
24. \(y_{p} = \cos x − \sin x;\: y = \cos x − \sin x + e^{4x} (c_{1} + c_{2}x)\)
25. \(y_{p} = \cos 2x − 2 \sin 2x;\: y = \cos 2x − 2 \sin 2x + c_{1} + c_{2}e^{−x}\)
26. \(y_{p}=\cos 3x;\: y=\cos 3x+e^{x}(c_{1}\cos\sqrt{2}x+c_{2}\sin\sqrt{2}x)\)
27. \(y_{p} = \cos x + \sin x;\: y = \cos x + \sin x + e^{−3x} (c_{1} \cos 2x + c_{2} \sin 2x)\)
28. \(y_{p} = −2 \cos 2x + \sin 2x;\: y = −2 \cos 2x + \sin 2x + c_{1}e^{−4x} + c_{2}e^{−3x};\: y = −2 \cos 2x + \sin 2x + 2e^{−4x} − 3e^{−3x}\)
29. \(y_{p} = \cos 3x − \sin 3x;\: y = \cos 3x − \sin 3x + e^{3x} (c_{1} + c_{2}x)\: y = \cos 3x − \sin 3x + e^{3x} (1 + 2x)\)
30. \(y=\frac{1}{\omega _{0}^{2}-\omega ^{2}}(M\cos\omega x+N\sin\omega x)+c_{1}\cos\omega_{0}x+c_{2}\sin\omega_{0}x\)
33. \(y_{p}=-1+2x+3x^{2}+\frac{e^{3x}}{3};\: y=-1+2x+3x^{2}+\frac{e^{3x}}{3}+c_{1}e^{-6x}+c_{2}e^{x}\)
34. \(y_{p} = 1 + x + e^{2x};\: y = 1 + x + e^{2x} (1 + c_{1}\cos x + c_{2}\sin x)\)
35. \(y_{p} = −x + x^{3} − 2e^{−2x};\: y = −x + x^{3} − 2e^{−2x} + c_{1}e^{−7x} + c_{2}e^{−x}\)
36. \(y_{p} = 1 − x^{2} + e^{x};\: y = 1 − x^{2} + e^{x} + e^{2x} (c_{1} + c_{2}x)\)
37. \(y_{p}=2x+x^{3}+\frac{4}{45}e^{x/2};\: y=2x+x^{3}+\frac{4}{45}e^{x/2}+e^{-x}(c_{1}\cos 3x+c_{2}\sin 3x)\)
38. \(y_{p} = 1 − x^{2} + e^{x};\: y = 1 − x^{2} + e^{x} + e^{2x} (1+c_{1}\cos x + c_{2}\sin x)\)