Teaching DSSSB TGT Mock Test 2025 Mathematical Science Ordinary Differential Equations Initial Value Problem
Let k be a positive integer. Consider the differential equation
\( \frac{d y}{d t}=y^{\frac{3 k}{ 3k+2}}\), k ∈ \(\mathbb N\), y(0) = 0, t > 0
Which of the following statements is true?
1
It has a unique solution which is continuously differentiable on (0, ∞)
2
It has at most two solutions which are continuously differentiable on (0, ∞).
3
It has infinitely many solutions which are continuously differentiable on (0, ∞).
4
It has no continuously differentiable solution on (0, ∞)