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Popular >

(dy)/(dx)=x*y

Solution

\frac{d y}{d x} = x \cdot y

Solution

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

Solution steps

\frac{d y}{d x} = x \cdot y

Solve separable ODE:

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

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

Popular Examples

y^'=3ye^t,y(0)=1

y^{^{'}} = 3 y e^{t}, y (0) = 1

(dy)/(dx)=x^2y-1.1y

\frac{d y}{d x} = x^{2} y - 1.1 y

y^'=((3x^2-1))/((3+2y))

y^{^{'}} = \frac{( 3 x ^{2} - 1 )}{( 3 + 2 y )}

(dy)/(dt)=(3t^2+4t+2)/(2(y-1)),y(0)=-1

\frac{d y}{d t} = \frac{3 t ^{2} + 4 t + 2}{2 ( y - 1 )}, y (0) = - 1

y^'=(e^{-x}-e^x)/(3+4y)

y^{^{'}} = \frac{e ^{- x} - e ^{x}}{3 + 4 y}

Frequently Asked Questions (FAQ)

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