Answer to Question #307907 in Differential Geometry | Topology for Johannes Steven

Question

1. Verify that (xy² -1) dx + (x²y) dy is exact and hence solve it.
2. Solve: dy/dx - y = e^2x , y(0) = 7
3. The differential equation of motion of a simple pendulum is given as d²x/dt² + g/l*x where x is the dependent variable and t is the independent variable. Find the displacement of the pendulum as a function of time t.  
4. Solve the equation y^//+ y^/- 2y- x² = 0