Solve 2y' = x y - ScanMath

Evaluate

2 y^{'} = x y

Rewrite the expression

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

Rewrite the expression

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

Multiply the terms

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

Multiply the terms

\frac{2}{y} \times \frac{d y}{d x} = x

Transform the expression

\frac{2}{y} \times d y = x d x

Integrate the left-hand side of the equation with respect to y and the right-hand side of the equation with respect to x

\int \frac{2}{y} d y = \int x d x

Calculate

More Steps

2 ln (y) + C_{1} = \int x d x, C_{1} \in R

Calculate

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2 ln (y) + C_{1} = \frac{x ^{2}}{2} + C_{2}, C_{1} \in R, C_{2} \in R

Since the integral constants C_{1} and C_{2} are arbitrary constants, replace them with constant C

2 ln (y) = \frac{x ^{2}}{2} + C, C \in R

Solution

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y = e^{\frac{x ^{2} + C}{4}}, C \in R

Solve the differential equation