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Popular >

(dy)/(dx)=kxy

Solution

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

Solution

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

Solution steps

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

Solve separable ODE:

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

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

Popular Examples

(dy)/(dx)=2xsqrt(y-1)

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

d y = e^{3 x - 2 y} d x

(dy)/(dx)=e^{3x}e^{2y}

\frac{d y}{d x} = e^{3 x} e^{2 y}

y(pdp)/(dy)-(p)^2+p=0

y \frac{p d p}{d y} - (p)^{2} + p = 0

(dy)/(dx)=(2x+sec^2(x))/(2y),y(0)=-2

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{2 y}, y (0) = - 2

Frequently Asked Questions (FAQ)

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