This is a second-order linear homogeneous differential equation. The characteristic equation has roots ±2i, leading to the solution y = C1 cos(2x) + C2 sin(2x).

Dividing both sides by 2 gives x - 1 = 2, thus x = 3.

Expanding gives 2x - 6 = 8. Adding 6 gives 2x = 14, thus x = 7.

2x + 3 = 7 => 2x = 4 => x = 2.

Adding 4 to both sides gives 2x = 14. Dividing by 2 gives x = 7.

2^x = 2^4, so x = 4.

Since 32 = 2^5, we have x = 5.

To solve for x, add 4 to both sides to get 3x = 9, then divide by 3 to find x = 3.

Subtract 1 from both sides: 4x = 8. Then divide by 4: x = 2.

Subtracting 8 from both sides gives 4x = 16. Dividing by 4 gives x = 4.

Adding 8 to both sides gives 4x = 8. Dividing by 4 gives x = 2.

Adding 7 to both sides gives 5x = 10, then dividing by 5 gives x = 2.

This is a separable differential equation. The solution is y = Ce^(-5x), where C is a constant.

This is a separable equation. Integrating gives y = 1/(C - x).

Factoring gives (x - 2)(x + 2) = 0, leading to solutions x = 2 and x = -2.

This is a separable equation. The solution is y = Ce^(-2x).

This is a first-order linear differential equation. The solution is y = Ce^(-3x).

This is a first-order linear equation. The integrating factor is e^(3x), leading to the solution y = Ce^(3x) + 2.

This is a separable equation. Integrating gives y = C/(C + x).

The characteristic equation is r^2 + 4 = 0, giving complex roots. The general solution is y = C1 cos(2x) + C2 sin(2x).

The characteristic equation r^2 - 3r + 2 = 0 has roots 1 and 2, leading to y = C1 e^(x) + C2 e^(2x).

The absolute value equation gives two cases: x - 3 = 5 or x - 3 = -5, leading to x = 8 or x = -2.

Using the integrating factor e^x, we solve to get y = e^x + Ce^(-x).

-2x + 4 > 0 => -2x > -4 => x < 2.

-2x + 5 > 1 => -2x > -4 => x < 2.

2x + 3 < 7 => 2x < 4 => x < 2.

2x + 5 > 3x - 1 => 6 > x => x < 6

3(x - 1) < 2(x + 2) => 3x - 3 < 2x + 4 => x < 7.

3x - 5 ≤ 4 => 3x ≤ 9 => x ≤ 3

4 - x < 2 => -x < -2 => x > 2.