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MathSofiya
 2 years ago
\[y''+6y'+9y=1+x\]
\[r_1=r_2=3\]
\[y_c=c_1e^{3x}+c_2xe^{3x}\]
\[y_p(x)=Ax+B\]
\[y_p'(x)=A\]
\[y_p''(x)=0\]
\[0+(9A)x+(6A+B)=1+x\]
\[A=\frac19\]
\[B=\frac13\]
\[y_p(x)=\frac19x+\frac13\]
\[y(x)=c_1e^{3x}+c_2e^{3x}+\frac19x+\frac13\]
how did I do?
MathSofiya
 2 years ago
\[y''+6y'+9y=1+x\] \[r_1=r_2=3\] \[y_c=c_1e^{3x}+c_2xe^{3x}\] \[y_p(x)=Ax+B\] \[y_p'(x)=A\] \[y_p''(x)=0\] \[0+(9A)x+(6A+B)=1+x\] \[A=\frac19\] \[B=\frac13\] \[y_p(x)=\frac19x+\frac13\] \[y(x)=c_1e^{3x}+c_2e^{3x}+\frac19x+\frac13\] how did I do?

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dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.1pretty good...i only see 1 thing it should be 0+(9A)x +(6A+9B) = 1+x 9(Ax +B) = (9A)x + 9B it only changes the B value to 1/27

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1oh thank you! silly me....hihi
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