Differential Equations — DU B.Sc. (Hons.) Mathematics Previous Year Question Papers

3. Both parts of the question to be attempted together. 1 (a) Show that y = 4e2* + 2e-3x is a solution of the initial-value problem (7.5) Is y = 2e2x + 4e-3* also a solution of this problem? Explain why or why not. (b) Solve the following initial value problem (7.5) (c) Solve the differential equation (7.5) 2 (a) Solve the differential equation (7.5) (b) Solve the differential equation (7.5) by first finding an integrating factor. (c) Find the orthogonal trajectories of the family of circles? + y2 = c. (7.5) 3 (a) Solve the initial value problem (b) Find the general solution of the following differential equation by using the (7.5) method of undetermined coefficients. (c) Use the method of variation of parameters to find the general solution of the (7.5) differential equation d'y 4 (a) Find the general solution of the differential equation (7.5) (b) Transform the following fourth-order ordinary differential equation into a system (7.5) of four first-order ordinary differential equation (c) Solve the linear system dx dy di + đt 5 (a) Find the general solution of the following differential equation (7.5) (b) Find the solution of the equation ux+yuy=xe*" (7.5) with Cauchy data u = 0 on y = x?. (c) Reduce the following equation into canonical form and find the general solution Solve the following initial value problem using the method of separation of variables (7.5) (b) Find the solution of the initial value systems (7.5) with ux,0) =x and u(x0) = x. (c) Obtain the general solution of (7.5)