Mastering First-Order Differential Equations

• y = Ce^(x)

• y = 3e^(x)

• y = Ce^(4x)

Find the general solution of dy/dx = y^2.

• y = x + C

• y = 1/(x + C)

• y = e^x + C

• y = -1/(x + C)

Solve the initial value problem: dy/dx = 2x, y(0) = 1.

• y = x^2 + 2

• y = x^2 - 1

• y = x^2 + 1

• y = 2x + 1

Determine the solution for dy/dx = -4y + 8.

• y = Ce^(4x) - 2

• y = 2 + Ce^(-4x)

• y = 8 - 2e^(4x)

• y = 4 - Ce^(4x)

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

• y = C/x

• y = Ce^(-2/x)

• y = Cx^2

• y = Ce^(2/x)

Find the particular solution of dy/dx = 5y with y(1) = 3.

• y = 3e^(5x)

• y = 3e^(5x - 1)

• y = 3e^(5x - 5)

• y = 3e^(5x + 5)

Solve the linear equation: dy/dx + 2y = 6.

• y = 3 + Ce^(-2x)

• y = 2x + 1

• y = 3 - Ce^(-2x)

• y = 6e^(2x)

Determine the solution for dy/dx = sin(x) + y.

• y = -cos(x) + Ce^(x)

• y = cos(x) + Ce^(x)

• y = -sin(x) + Ce^(x)

• y = sin(x) + Ce^(x)

Solve the equation dy/dx = e^x - y with y(0) = 1.

• y = (1/3)e^x + (2/3)e^(-x)

• y = (1/2)e^x + (1/2)e^(-x)

• y = e^(-x) - 1

• y = e^x + 1

Find the general solution of dy/dx = (x + y)/(x - y).

• x + y = k(x - y)

• dy/dx = (x - y)/(x + y)

• y = kx + c

• x - y = k(x + y)