System of Differential equations - 2nd order - undetermined coefficients

System of Differential equations - 2nd order - undetermined coefficients

System of Differential equations - 3rd order - undetermined coefficients

Reduction of Order formula - Second solution (1 - 2x - x^2) y'' + 2(1 + x)y' - 2y = 0 , y1(x) = x + 1

Solution

Second order differential equation using variation of parameters with constant coefficients

y'' + 2y' + y = e^(-x)/(1 + x^2)

Non homogeneous Differential Equation using Undetermined Coefficients

y'' - y' - 6y = e^(-t)

Non homogeneous Differential Equation using Undetermined Coefficients

y'' - y' - 6y = t^2 - 3t

Euler Method

Use the Euler method with two steps to approximate y(1), where y' = (1 + x)y + x^ 2 , y(0) = 1



Solution

Differential Equation Laplace Transform (Dirac Delta Function)

Homogeneous Differential Equation using Laplace Transform

y'' - 3y' - 28y = 0 , y(0) = 5 , y'(0) = 7

Convolution Theorem (Laplace Transform)