Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Ordinary Differential Equations Wronskians
Let u1, u2, ... un be n linearly independent solutions of the linear differential equation of order n P0(x)y(n) + P1(x)y(n-1) + ... + Pn(x)y = 0, P0(x) ≠ 0.
Let W be the Wronskian of the solution u1, u2, ... un and W0 be the value of W at x = x0. Then which of the following is true?
1
\(W=W_{0} \exp \left\{\displaystyle\int_{x_{0}}^{x} \frac{P_{1}(x)}{P_{0}(x)} d x\right\}\)
2
\(W=W_{0} \exp \left\{\displaystyle \int_{x_{0}}^{x} \frac{P_{n}(x)}{P_{0}(x)} d x\right\}\)
3
\(W=W_{0} \exp \left\{\displaystyle -\int_{x_{0}}^{x} \frac{P_{1}(x)}{P_{0}(x)} d x\right\}\)
4
\(W=W_{0} \exp \left\{\displaystyle -\int_{x_{0}}^{x} \frac{P_{n}(x)}{P_{0}(x)} d x\right\}\)
5
Question Not Attempted