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#### karush

##### Well-known member

- Jan 31, 2012

- 2,928

$$y^\prime + (1/x)y=\sin x \quad x>0, \qquad \color{red}

{\frac{c}{x}+\frac{\sin x}{x}-\cos x} $$

ok first $u=1/x$ and $x=1/u$ then

$$u(x) = \exp\int u \, du = e^{\ln(u)}=u +c$$

proceed or ???

$\tiny{Elementary Differential Equations And Boundary Value Problems, \\

By: William E. Boyce and Richard C. Diprima \\

1969, Second Edition}$