Higher-order linear equations

Concepts

• Second-order linear equation 10 exercisesIt is a second-order differential equation, linear in the unknown y and its derivatives, whose coefficients p, q and term g depen…
• Superposition principle 10 exercisesIt states that if y_1 and y_2 are solutions of a linear homogeneous equation L[y]=0, every linear combination of them with consta…
• Wronskian 10 exercisesThe Wronskian W of two differentiable functions y_1 and y_2 is the determinant of the matrix formed by them and their first deriv…
• Characteristic equation 10 exercisesThe characteristic equation of ay''+by'+cy=0, with constant coefficients a,b,c, is the algebraic equation in the unknown r that r…
• Undetermined coefficients 10 exercisesA method that finds a particular solution y_p of ay''+by'+cy=g(t) by guessing a function of the same type as g, with coefficients…
• Variation of parameters 10 exercisesA method that builds a particular solution y_p of y''+py'+qy=g(t) from two homogeneous solutions y_1,y_2 and their Wronskian W, b…
• Harmonic oscillator 10 exercisesModel of a mass m attached to a spring of constant k, with no friction or external force, whose position y(t) oscillates with ang…