Mathematics: Solve the boundary value problem

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Solve the boundary value problem - id4242900, makennahudson94

Ответ:

lol4373

13.01.2022

Mathematics

Characteristic equation:

$r^2+4r-5=(r+5)(r-1)=0\implies r=-5,r=1$

$\implies y_c=C_1e^{-5x}+C_2e^x$

Given that y(0)=0

and $y\left(\dfrac\pi2\right)=1$ , you have

$\begin{cases}0=C_1+C_2\\1=C_1e^{-5\pi/2}+C_2e^{\pi/2}\end{cases}\implies C_1=\dfrac{e^{5\pi/2}}{1-e^{3\pi}},C_2=-\dfrac{e^{5\pi/2}}{1-e^{3\pi}}$

so that the particular solution is

$y=\dfrac{e^{5\pi/2}}{1-e^{3\pi}}(e^{-5x}-e^x)$

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Ответ:

sabrinabowers4308

04.12.2021

Mathematics

Step-by-step explanation:

i am smart

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Solve the boundary value problem

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