en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

xy^'+y=e^x,y(1)=3

Solution

x y^{^{'}} + y = e^{x}, y (1) = 3

Solution

y = \frac{e ^{x}}{x} + \frac{3 - e}{x}

Solution steps

x y^{'} (x) + y = e^{x}

Solve linear ODE:

y = \frac{e ^{x}}{x} + \frac{3 - e}{x}

y = \frac{e ^{x}}{x} + \frac{3 - e}{x}

Popular Examples

limit as x approaches 0 of x^2sin(x^2)

x \to 0 lim (x^{2} sin (x^{2}))

derivative of x^3cos(3x)

\frac{d}{d x} (x^{3} cos (3 x))

integral of (8e^{8y})/(6+e^{8y)}

\int \frac{8 e ^{8 y}}{6 + e ^{8 y}} d y

integral of (sqrt(2x^2-3))/(x^2)

\int \frac{2 x ^{2} - 3}{x ^{2}} d x

2x^2*(dy)/(dx)=piysin(pi/(2x))

2 x^{2} \cdot \frac{d y}{d x} = π y sin (\frac{π}{2 x})

Frequently Asked Questions (FAQ)

What is the solution for xy^'+y=e^x,y(1)=3 ?
The solution for xy^'+y=e^x,y(1)=3 is y=(e^x)/x+(3-e)/x