What is the solution for (dy)/(dx)=-1/2 y+x ?

The solution for (dy)/(dx)=-1/2 y+x is y=2x-4+(c_{1})/(e^{x/2)}

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(dy)/(dx)=-1/2 y+x

\frac{d y}{d x} = - \frac{1}{2} y + x

y = 2 x - 4 + \frac{c _{1}}{e ^{\frac{x}{2}}}

Solution steps

\frac{d y}{d x} = - \frac{1}{2} y + x

Solve linear ODE:

y = 2 x - 4 + \frac{c _{1}}{e ^{\frac{x}{2}}}

y = 2 x - 4 + \frac{c _{1}}{e ^{\frac{x}{2}}}

\int \frac{ln ( x )}{2} d x

d er i v a t i v e cos^{2} (3 x)

\int 6 x^{\frac{2}{3}} - 8 x^{\frac{3}{4}} d x

x \to 1 + lim (ln (x))

\frac{d ^{2}}{d x ^{2}} (e^{5 e^{x}})

What is the solution for (dy)/(dx)=-1/2 y+x ?
The solution for (dy)/(dx)=-1/2 y+x is y=2x-4+(c_{1})/(e^{x/2)}