Answer to Question #199494 in Differential Equations for Raj Kumar

Question

Classify the following as true or false give reasons for your answers.

i) For the Initial Value Problem, dy/dx = f(x,y), y(x₀)=y₀, the continuity of f(x,y) and ∂f/∂y guarantees the unique solution of the problem.

ii) Equations (d²y/dx²) - 2x(dy/dx) + x²y = e^{(x^2)/2} and d²y/dx² +y = 1 have the same normal form.

iii) Equation cos(x+y)p + sin(x+y)q = z² + z is a quasi-linear equation

iv) (∂²z/∂x²)(∂²z/∂y²) - (∂²z/∂x∂y)² = 0 is a non-linear Partial Differential Equation.

v) Every solution of the Ordinary Differential Equation (D²+1)²y = 0 is bounded on [0,∞[ .