1. The problem statement, all variables and given/known data
Solve the differential equation
x(dy/dx) -4y = x^4e^x
2. Relevant equations
3. The attempt at a solution
So this is what I did.
dy/dx -4y/x = x^3e^x
Then I did the integral of P(x) which I said was 4/x so the integral is lnx^4 then I(x) = e^lnx^4 = x^4. I then multiplied through by this and got
x^4(dy/dx) - 4x^3(y) = x^7e^x I said my product rule for my left side was (x^4(y))' so I ended up with x^4(y) = ∫ x^7(e^x) I just used a reduction formula for the integral. But is my procss OK? THanks
my equation b
Solve the differential equation
x(dy/dx) -4y = x^4e^x
2. Relevant equations
3. The attempt at a solution
So this is what I did.
dy/dx -4y/x = x^3e^x
Then I did the integral of P(x) which I said was 4/x so the integral is lnx^4 then I(x) = e^lnx^4 = x^4. I then multiplied through by this and got
x^4(dy/dx) - 4x^3(y) = x^7e^x I said my product rule for my left side was (x^4(y))' so I ended up with x^4(y) = ∫ x^7(e^x) I just used a reduction formula for the integral. But is my procss OK? THanks
my equation b
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