Consider the initial value problem dy dx = x 2 + y 2 , y(0) = 1; 0 ≤ x ≤ 1. Then which of the following statements is true?

The solution becomes unbounded in some subinterval of [π/4, 1]

The solution exhibits a singularity at some point in [0, 1]

Every solution is bounded in [0, π/4]

Consider the initial value problem dy dx = x 2 + y 2 , y(0) = 1; 0 ≤ x ≤ 1. Then which of the following statements is true?

The solution becomes unbounded in some subinterval of [π/4, 1]

The solution exhibits a singularity at some point in [0, 1]

Every solution is bounded in [0, π/4]

Consider the initial value problem dy dx = x 2 + y 2 , y(0) = 1;... | Mathematics MCQ [Updated November 2026] | GkGet

Mathematics · Differential Equations

Consider the initial value problem dydx = x² + y², y(0) = 1; 0 ≤ x ≤ 1. Then which of the following statements is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1The solution becomes unbounded in some subinterval of [π/4, 1]
2The solution exhibits a singularity at some point in [0, 1]
3Every solution is bounded in [0, π/4]
4There exists a unique solution in [0, π/4]✓

Correct answer

There exists a unique solution in [0, π/4]

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