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Popular >

(dy)/(dx)+y=e^x

Solution

\frac{d y}{d x} + y = e^{x}

Solution

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

Solution steps

\frac{d y}{d x} + y = e^{x}

Solve linear ODE:

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

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

Popular Examples

derivative of f(x)=-(6x^2)/((x^3-1)^2)derivative of

f (x) = - \frac{6 x ^{2}}{( x ^{3} - 1 ) ^{2}}

derivative of (x+1^{2/3}(2x^2-1)^3)

\frac{d}{d x} ((x + 1)^{\frac{2}{3}} (2 x^{2} - 1)^{3})

derivative of sin(kx)

\frac{d}{d x} (sin (k x))

derivative of 2/((4-x^2))

\frac{d}{d x} (\frac{2}{( 4 - x ) ^{2}})

integral of 2u^2

\int 2 u^{2} d u

Frequently Asked Questions (FAQ)

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