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Popular >

(dy)/(dx)+xy=e^xy

Solution

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

Solution

y = e^{e^{x} - \frac{x ^{2}}{2} + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{e^{x} - \frac{x ^{2}}{2} + c_{1}}

y = e^{e^{x} - \frac{x ^{2}}{2} + c_{1}}

Popular Examples

derivative of ((x^4-4x+3)/(sqrt(x)+1))

\frac{d}{d x} (\frac{( x ^{4} - 4 x + 3 )}{x + 1})

tangent of f(x)=x^2+4,\at x=1 tangent of

f (x) = x^{2} + 4, at x = 1

tangent of f(x)=x^5-3(x)^3+6 tangent of

f (x) = x^{5} - 3 (x)^{3} + 6

derivative of 6x^5(x^4-8)derivative of

6 x^{5} (x^{4} - 8)

inverse oflaplace ((2s+13))/(s^2+4s+13)inverse laplace

\frac{( 2 s + 13 )}{s ^{2} + 4 s + 13}

Frequently Asked Questions (FAQ)

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