### Questions (49)

 16 Do eigenvalues depend on the choice of basis? 4 linearly independent solution to second order ODE. 3 Eigenvalues of a complex $4 \times 4$ Matrix 3 Proof that: $(a-b)\cdot\Bigg(\sum_{k=0}^{n}a^{n-k}b^{k}\Bigg)=a^{n+1}-b^{n+1}\text{ }\forall n\in\mathbb{N_{0}}$ 3 Limit of $\sqrt{n^{3}+n^{2}}-n$.

### Reputation (488)

 +5 Exact ODE: show that $y$ is a solution iff it is in a level set of $F$ +10 Solve ODE initial value problem: $\dot{u}=(2t+u-3)^2-2 , u(1)=0$ Separation of variables fails +20 linearly independent solution to second order ODE. +5 Solve initial value problem $u^{'}(t)=\frac{2(u(t))^{2}}{3(t+1)^{2}}$, $\ u(1)=3$

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