Question

solve(D^3-5D^2+8D-4)y=e2x​

Answer 1

Answer:

What is the general solution to (D^3-5D^2+8D-4) y=e^2x?

For the equation ( D^3 -5D^2 +8D -4)y = e^2x ,the characteristic equation is

m^3 -5m^2 +8m -4 = ( m-1)( m-2)^2 =0 , roots 1 , 2 ,2 .The complementary

function is yh = C1e^x + C2e^2x + C3xe^2x .

For the particular integral is appropriate the function yp = A(x^2)e^2x.

substituting in the equation gives A = 1/2 .Therefore the required solution is

y = C1e^x + C2e^2x + C3xe^2x +(1/2)(x^2)e^2x .

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Answer 2

Answer:

ꜱɪᴍᴘʟɪꜰʏɪɴɢ

(ᴅ3 + -5ᴅ + 8ᴅ + -4) * ʏ = ᴇ2x

ʀᴇᴏʀᴅᴇʀ ᴛʜᴇ ᴛᴇʀᴍꜱ:

(-4 + -5ᴅ + 8ᴅ + ᴅ3) * ʏ = ᴇ2x

ᴄᴏᴍʙɪɴᴇ ʟɪᴋᴇ ᴛᴇʀᴍꜱ: -5ᴅ + 8ᴅ = 3ᴅ

(-4 + 3ᴅ + ᴅ3) * ʏ = ᴇ2x

ʀᴇᴏʀᴅᴇʀ ᴛʜᴇ ᴛᴇʀᴍꜱ ꜰᴏʀ ᴇᴀꜱɪᴇʀ ᴍᴜʟᴛɪᴘʟɪᴄᴀᴛɪᴏɴ:

ʏ(-4 + 3ᴅ + ᴅ3) = ᴇ2x

(-4 * ʏ + 3ᴅ * ʏ + ᴅ3 * ʏ) = ᴇ2x

(-4ʏ + 3ʏᴅ + ʏᴅ3) = ᴇ2x

ꜱᴏʟᴠɪɴɢ

-4ʏ + 3ʏᴅ + ʏᴅ3 = ᴇ2x

ꜱᴏʟᴠɪɴɢ ꜰᴏʀ ᴠᴀʀɪᴀʙʟᴇ 'ʏ'.

ᴍᴏᴠᴇ ᴀʟʟ ᴛᴇʀᴍꜱ ᴄᴏɴᴛᴀɪɴɪɴɢ ʏ ᴛᴏ ᴛʜᴇ ʟᴇꜰᴛ, ᴀʟʟ ᴏᴛʜᴇʀ ᴛᴇʀᴍꜱ ᴛᴏ ᴛʜᴇ ʀɪɢʜᴛ.

ʀᴇᴏʀᴅᴇʀ ᴛʜᴇ ᴛᴇʀᴍꜱ:

-1ᴇ2x + -4ʏ + 3ʏᴅ + ʏᴅ3 = ᴇ2x + -1ᴇ2x

ᴄᴏᴍʙɪɴᴇ ʟɪᴋᴇ ᴛᴇʀᴍꜱ: ᴇ2x + -1ᴇ2x = 0

-1ᴇ2x + -4ʏ + 3ʏᴅ + ʏᴅ3 = 0

ᴛʜᴇ ꜱᴏʟᴜᴛɪᴏɴ ᴛᴏ ᴛʜɪꜱ ᴇQᴜᴀᴛɪᴏɴ ᴄᴏᴜʟᴅ ɴᴏᴛ ʙᴇ ᴅᴇᴛᴇʀᴍɪɴᴇᴅ.

Step-by-step explanation:

ᎻϴᏢᎬ ᎷᎽ ᎪΝՏᏔᎬᎡ ᏆՏ ᎻᎬᏞᏢҒႮᏞ ҒϴᎡ ᎽϴႮ (◕ᴗ◕✿)