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Popular Calculus >

y(dy)/(dx)+3y=x^2y

Solution

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

Solution

y = \frac{x ^{3}}{3} - 3 x + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y y^{^{'}} (x) + 3 y = x^{2} y

Isolate

y^{'} (x) : y^{'} (x) = x^{2} - 3

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int x^{2} - 3 d x

\int x^{2} - 3 d x = \frac{x ^{3}}{3} - 3 x + c_{1}

y = \frac{x ^{3}}{3} - 3 x + c_{1}

Graph

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Frequently Asked Questions (FAQ)

What is the solution for y(dy)/(dx)+3y=x^2y ?
The solution for y(dy)/(dx)+3y=x^2y is y=(x^3)/3-3x+c_{1}