For \(y'=xy^2\), what is \(\partial f/\partial y\)?

Study Differential equations in ZWMath →

Review the concept: Existence and uniqueness theorem

The existence and uniqueness theorem guarantees that an initial value problem has a unique solution near the initial point, if the equation and its partial derivative with respect to the unknown are continuous there.

More practice problems: existence and uniqueness theorem

• ZW-EXISTENCE-AND-UNIQUENESS-THEOREM-002 For which initial value problem does the theorem guarantee a unique solution?
• ZW-EXISTENCE-AND-UNIQUENESS-THEOREM-003 The problem y'=√y,\ y(0)=0 has the solution y=0. Which of these functions, for x≥ 0, is another sol…
• ZW-EXISTENCE-AND-UNIQUENESS-THEOREM-004 For y'=(y)/(x-3), where do f and ∂ f/∂ y stop being continuous?
• ZW-EXISTENCE-AND-UNIQUENESS-THEOREM-005 If f and ∂ f/∂ y are continuous near (x_0,y_0), the theorem ensures that the initial value problem:
• ZW-EXISTENCE-AND-UNIQUENESS-THEOREM-006 For y'=x+y^2, can two different solutions cross?
• ZW-EXISTENCE-AND-UNIQUENESS-THEOREM-007 The solution of y'=y^2,\ y(0)=1 is y=(1)/(1-x). What is the largest interval containing 0 on which…
• ZW-EXISTENCE-AND-UNIQUENESS-THEOREM-008 For y'=3y^2/3, the set of initial points (x_0,y_0) where the theorem guarantees a unique solution i…
• ZW-EXISTENCE-AND-UNIQUENESS-THEOREM-009 The hypotheses of the theorem fail for an initial value problem. What can be concluded?

ZW-EXISTENCE-AND-UNIQUENESS-THEOREM-002 →