1.1 Problems In Problems 1 through 12, verify by substitution that each given function is a...

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1.1 Problems In Problems 1 through 12, verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with re- spect to x. 1. y' = 3x²; y = x³ +7 2. y' + 2y = 0; y = 3e-2x 3. y" +4y=0; y₁ = cos 2x, y₂ = sin 2x 4. y"=9y: y₁=e³, y₂ = e-³ 5. y'=y+2e;y=e¹ - e 6. y" +4y + 4y = 0; y₁=e-2x, y₂ = xe-²x 7. y" - 2y + 2y = 0; y₁= e cos x, y₂ = e sinx 8. y"+y = 3 cos 2x, y₁ = cos.x-cos 2x, y2 = sinx-cos2x 9. y' + 2xy² = 0; y = 1 1+x² 10. x²y + xy-y = ln x; y₁=x-In x, y₂ = 117x²y" +5xy + 4y = 0; y₁=32=2 X Inx -In x 1.1 Problems In Problems 1 through 12, verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with re- spect to x. 1. y' = 3x²; y = x³ +7 2. y' + 2y = 0; y = 3e-2x 3. y" +4y=0; y₁ = cos 2x, y₂ = sin 2x 4. y"=9y: y₁=e³, y₂ = e-³ 5. y'=y+2e;y=e¹ - e 6. y" +4y + 4y = 0; y₁=e-2x, y₂ = xe-²x 7. y" - 2y + 2y = 0; y₁= e cos x, y₂ = e sinx 8. y"+y = 3 cos 2x, y₁ = cos.x-cos 2x, y2 = sinx-cos2x 9. y' + 2xy² = 0; y = 1 1+x² 10. x²y + xy-y = ln x; y₁=x-In x, y₂ = 117x²y" +5xy + 4y = 0; y₁=32=2 X Inx -In x

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