Assignment No.2 MATHS

Chemistry A

Qu.1)  Solve by method of variation of parameters

                    y” – 2y’ = e^x sin x

Qu.2)  Solve by the method of variation of parameters

                   d²y/dx² + (1-cot x) dy/dx – y cot x = sin²x

Qu.3)  Solve x²d²y/dx² + x dy/dx + (log x) sin (log x)

Qu.4)  Solve x³ d³y/dx³ + 3x² d²y/dx² + x dy/dx + y = x + log x

Qu.5) Obtain general sol. of the diff. equation

                        x²y” + xy’ – y = x³e^x

Qu.6)  Solve   dx/dy – 7x + y = 0 ………….(i)

                      dy/dt – 2x - 5y = 0 ..……….(ii)

Qu.7)  Solve   dx/dy + dy/dt – 2y = 2cos t – 7 sin t

                      dx/dt + dy/dt – 2x = 4cos t – 3 sin t

Qu.8)  Solve the following system of differential equations

                     dx/dt + dy/dt + 3x = sin t   

                     dx/dt + y - x = cos t     

Qu.9)  A particle whose mass is m is acted upon by a force mμ (x + a⁴/x³)

           towards the origin. If it starts from reset at a distance a, show that it will

           arrive at the origin in time л/ 4√μ

Qu.10)  Solve   y (1 – log y) d²y/dx² + (1 + log y) (dy/dx)² = 0

Qu.11)  Solve   x² d²y/dx² – 2x (1+x) dy/dx + 2 (1+x) y = x³

Qu.12)  Solve   d²y/dx² – 1/x dy/dx + 4x²y = x⁴