Selected Topics in Partial Differential Equations
www.diva-portal.org › smash › getThe general topic of this Ph.D. thesis is partial differential equations (PDEs). This thesis deals with various problems originating in quantum mechanics and quantum chemistry. Also, problems within nonlinear analysis are studied. The introduction that follows is brief and by no means complete. For a more com-plete description the reader may consult the bibliography within each paper. 1.1 The time-independent Schrödinger equation
16 Additional Topics in Differential Equations
www.larsoncalculus.com › calc11 › wp-content1134 Chapter 16 Additional Topics in Differential Equations Finding an Integrating Factor Solve the differential equation (y2 − x) dx + 2y dy = 0. Solution This equation is not exact because M y (x, y) = 2y and N x (x, y) = 0. However, because M y (x, y) − N x (x, y) N(x, y) = 2y − 0 2y = 1 = h(x) it follows that e∫h(x) dx = e∫ dx = ex is an integrating factor. Multiplying the differential