1. Show that \(e^t\) and \(e^{-t}\) are solutions of \(y''-y=0\). Show that \(C_1e^t+C_2e^{-t}\) is also a solution. View Solution
2. Show that \(y_1=e^x\cos x\) and \(y_2=e^{x}\sin x\) are solutions of \(y''-2y'+2y=0\). View Solution
3. State the Principle of Superposition and verify it for \(y''-5y'-6y=0 \). View Solution
4. Find the Wronskian of the pair: \(t, te^{t} \). View Solution
5. Find the Wronskian of the pair: \(e^t \sin t, e^t \cos t \). View Solution
6. Show that \(\{\cosh t, \sinh t\}\) is a fundamental set for \(y''-y=0 \). View Solution
7. If the Wronskian of \(f\) and \(g\) is \(-4e^{t} \) and \(f=e^{2t}\), find \(g\). View Solution
8. If \(W(f, g) = t^2e^t \) and \(f(t)=t\), find \(g(t)\). View Solution