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Popular >

expand (dy)/(dx)+y(xe^{x^2}+1)

Solution

\frac{d}{d x} (+ y (x e^{x^{2}} + 1))

Solution

\frac{d y}{d x} (x e^{x^{2}} + 1) + (2 e^{x^{2}} x^{2} + e^{x^{2}}) y

Solution steps

\frac{d}{d x} (y (x e^{x^{2}} + 1))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = x e^{x^{2}} + 1

= \frac{d y}{d x} (x e^{x^{2}} + 1) + \frac{d}{d x} (x e^{x^{2}} + 1) y

\frac{d}{d x} (x e^{x^{2}} + 1) = 2 e^{x^{2}} x^{2} + e^{x^{2}}

= \frac{d y}{d x} (x e^{x^{2}} + 1) + (2 e^{x^{2}} x^{2} + e^{x^{2}}) y

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Frequently Asked Questions (FAQ)

What is the expand (dy)/(dx)+y(xe^{x^2}+1) ?
The expand (dy)/(dx)+y(xe^{x^2}+1) is (dy)/(dx)(xe^{x^2}+1)+(2e^{x^2}x^2+e^{x^2})y
What is the first expand (dy)/(dx)+y(xe^{x^2}+1) ?
The first expand (dy)/(dx)+y(xe^{x^2}+1) is (dy)/(dx)(xe^{x^2}+1)+(2e^{x^2}x^2+e^{x^2})y