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Solve the given initial-value problem. dy dx = x + 2y, y(0) = 7

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(\mathrm dy)/(\mathrm dx)=x+2y

(\mathrm dy)/(\mathrm dx)-2y=x

e^(-2x)(\mathrm dy)/(\mathrm dx)-2e^(-2x)y=xe^(-2x)

(\mathrm d)/(\mathrm dx)[e^(-2x)y]=xe^(-2x)

e^(-2x)y=\displaystyle\int xe^(-2x)\,\mathrm dx

e^(-2x)y=-\frac14e^(-2x)(1+2x)+C

y=-\frac{1+2x}4+Ce^(2x)


y(0)=7

7=-\frac{1+2\cdot0}4+Ce^(2\cdot0)

7=-\frac14+C

C=\frac{29}4


y=-\frac{1+2x}4+\frac{29}4e^(2x)
User Esteban Herrera
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