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Popular >

y^'+axy=0

Solution

y^{^{'}} + a x y = 0

Solution

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

Solution steps

y^{'} (x) + a x y = 0

Solve separable ODE:

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

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

Graph

Popular Examples

e^2x^'+xe^2+6xx^'=0

e^{2} x^{^{'}} + x e^{2} + 6 x x^{^{'}} = 0

(dy)/(dx)=4y^{-2}(x^6+x^4+x^2)

\frac{d y}{d x} = 4 y^{- 2} (x^{6} + x^{4} + x^{2})

(A+B)dy=C(x/y)dx

(A + B) d y = C (\frac{x}{y}) d x

(dy)/(dx)=(10+12x)/(xy^2)

\frac{d y}{d x} = \frac{10 + 12 x}{x y ^{2}}

(dv)/(dt)=60-8/100 v

\frac{d v}{d t} = 60 - \frac{8}{100} v

Frequently Asked Questions (FAQ)

What is the solution for y^'+axy=0 ?
The solution for y^'+axy=0 is y=e^{-(ax^2)/2+c_{1}}