Differential Equations 2024 Questions and Answers
Differential Equations 2024 Questions and Answers What are ODE (Ordinary Differential Equations) - Answer-An equation which is defined for functions with only one independent variable What is a linear differential equation? - Answer-A DE in which the unknown function is always linear How can you solve a Differential Equation - Answer-Analytically (Integrating) Geometrically (Integration Curve) Equazioni Differenziali a Variabili Separabili - Answer-y'(x) = a(x)*b(y(x)) Forma generale di un'equazione differenziale di primo grado - Answer-y'(x) = a(x,y(x))/b(x,y(x)) Solution of: (NHDE) y'(x) + p(x)y(x) = q(x) - Answer-y(x) = I(x) * ( int(I(x)q(x)) + c ) I(x) = e ^ int(p(x)) Show that the solution of a y'(x) + a(x)y(x) = b(x) is 1/I(x) int(I(x)b(x)) - Answer-Solve Homogeneous and then divide by the solution Prove Bernoulli ODE Solution - Answer-u = y^(1-n) If y1 and y2 are two linearly independent solutions of a second order linear and homogeneous differential equation. What are the general solutions? - Answer-y(x) = c1 y1(x) + c2 y2(x)
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