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2022年6月18日 · I have been trying to solve the differential equation $t y''(t) +2 y'(t) - ty(t)=0$ through the Frobenius method. WolframAlpha says the solution should be $ y(t) = c_1 \frac{e^{-t}}{t} + c_2\frac{e^t}{t}$ .

2020年8月9日 · I can solve Euler $t^2 y''+t y' + y=0$ and $y''+p(t) y'(t) + q(t) y=0$ where it is possible to convert it to constant coefficient using known transformation. But this ODE is not one of these two types.

2016年10月25日 · My book says that $y_1 = t, y_2 = te^t$ are solutions to the homogeneous equation. I'm trying a solution of the form $Y = u_1t+u_2te^t$, so the wronskian is $$W(t, te^t) = t^2e^t$$

y(t)的理想形式是 \[y(t)=(at+b){{e}^{st}}\] 。 请注意，尽管驱动项里没有单独的 \[{{e}^{st}}\] ，但是 t{{e}^{st}} 导数里会出现有，因此解函数中出现了 \[b{{e}^{st}}\] 。

y''-2y'+y=t\\ 对应的 齐次方程 的 特征根 为 r_1=r_2=1 ，对应的 通解 为 \color{red}{\bar y=(C_1+C_2t)e^t}\\ 而对于原方程，其 约束项 为

2×YT培养基是分子生物学常用培养基，可用于多种细菌培养。 2×YT培养基主要由胰蛋白胨、酵母提取物、氯化钠等组成，其浓度比常规LB培养基高。 其中酵母提取物为微生物生长提供碳源和能源，蛋白胨主要提供氮源，NaCl提供无机盐。 2×YT培养基是分子生物学常用培养基，可用于多种细菌培养。 2×YT培养基主要由胰蛋白胨、酵母提取物、氯化钠等组成，其浓度比常规LB培养基高。 其中酵母提取物为微生物生长提供碳源和能源，蛋白胨主要提供氮源，NaCl提供无机盐。 …

$$y{\left(t \right)} - 2 \frac{d}{d t} y{\left(t \right)} + \frac{d^{2}}{d t^{2}} y{\left(t \right)} = t e^{t}$$ Esta ecuación diferencial tiene la forma: y'' + p*y' + q*y = s,

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Use the Laplace transform to solve the given initial-value problem. y' + 3y = e6t, y(0) = 2 y(t) =