In big words. BERNOULI'S
$$y'+\frac{y}{t}=t \ln t$$
Integrating Factor: $e^{\int\frac{dt}{t}}=t$
$$\int d(yt)=\int t^2\ln t.dt+C $$
To solve $\int t^2 \ln t$, take $t=e^x$ and proceed.
This shall give your answer
$$\int e^{2x}.x=\frac{1}{2}(x.e^{2x}-e^{2x})$$
0
Suppose f is a zero divisor. Choose polynomial $g = b_0 + b_1x + \ldots + b_mx^m$ of least degree m such that $fg = 0 \implies \Sigma_{k \geq 0} \Sigma_{i + j = k} a_i b_j x^k = 0$.
From the formula of multiplication of two polynomials we must have $a_nb_m = 0 \implies a_n g = 0$ (Because $a_n g$...
0
Suppose f is a zero divisor. Choose polynomial $g = b_0 + b_1x + \ldots + b_mx^m$ of least degree m such that $fg = 0 \implies \Sigma_{k \geq 0} \Sigma_{i + j = k} a_i b_j x^k = 0$.
From the formula of multiplication of two polynomials we must have $a_nb_m = 0 \implies a_n g = 0$ (Because $a_n g$...
