First Order Differential Equations

Use an integrating factor to solve the equation dy/dx + 2y = 4x.

• y = x^2 + Ce^(2x)

• y = 2x - 1 + Ce^(-2x)

• y = 4x + C

• y = 2x^2 - 1 + Ce^(x)

Solve the first order linear differential equation: y' + 3y = 6.

• y = 6 - Ce^(3x)

• y = 3x + C

• y = 2 + Ce^(-3x)

• y = 2 - Ce^(-3x)

Use an integrating factor to solve: y' - 5y = 10.

• y = 10 + Ce^(5x)

• y = 2 + Ce^(5x)

• y = 5 + Ce^(-5x)

• y = -2 + Ce^(5x)

Solve the separable equation: dy/dx = (y^2 + 1)/(x^2).

• y = sin(-1/x + C)

• y = e^(1/x + C)

• y = cos(-1/x + C)

• y = tan(-1/x + C)

Find the general solution of the equation dy/dx = (3x^2)/(2y).

• y = ±√(x^3 + C)

• y = 3x^2 + C

• y = x^3 + C

• y = ±(2y^2 + 3x)