Using the integrating factor method, we find the solution to be y = (3/5) + Ce^(5x).

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).

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.

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).

For a monatomic ideal gas, the specific heat at constant volume (Cv) is 3R/2.

Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 10°C) = 25 J/kg°C.

Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 5°C) = 50 J/kg°C.

Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 5°C) = 50 J/kg°C

The specific heat capacity of air is approximately 1.005 J/kg·K.

The specific heat capacity of iron is approximately 0.45 J/g·K.

The specific heat capacity of water at constant pressure is approximately 4.18 J/g°C.

The specific heat capacity of water is defined as the amount of heat required to raise the temperature of 1 kg of water by 1°C, which is given as 4200 J/kg°C.

The specific heat capacity of water is approximately 4.18 J/g°C.

The speed of light in vacuum is approximately 3 x 10^8 m/s.

The modulus is √(1^2 + 2^2) = √(1 + 4) = √5. The square of the modulus is 5.

The modulus is √(1^2 + 1^2) = √2, and the square of the modulus is 2.

The square root of 64 is 8.

The square root of -1 is defined as i.

The square root of -4 is √(-1) * √4 = 2i.

The standard electrode potential for Zn²⁺/Zn is -0.76 V.

The standard electrode potential of the hydrogen electrode is defined as 0 V.

The standard enthalpy change for the formation of water from its elements (H2 and O2) is -285.83 kJ/mol.

The standard enthalpy change for combustion reactions, such as the formation of CO2 from carbon and oxygen, is typically negative, indicating that the reaction is exothermic.

The standard reduction potential indicates the tendency of a species to gain electrons, thus being reduced.

The standard reduction potential for the half-reaction Cu2+ + 2e- → Cu is +0.76 V, indicating a strong tendency to gain electrons.

The standard reduction potential for the half-reaction Fe^3+ + 3e- → Fe is +0.77 V, indicating a strong tendency to gain electrons.