Solve u = u' v - Socratic AI (ScanMath)

Evaluate

u = (u)^{'} \times v

Simplify

More Steps

u = v

Remove the parentheses

u = u^{'} v

Use the commutative property to reorder the terms

u = v u^{'}

Rewrite the expression

v u^{'} = u

Rewrite the expression

v \frac{d u}{d v} = u

Rewrite the expression

\frac{1}{u} \times v \frac{d u}{d v} = u \times \frac{1}{u}

Multiply the terms

\frac{1}{u} \times v \frac{d u}{d v} = 1

Rewrite the expression

\frac{1}{u} \times \frac{d u}{d v} = \frac{1}{v}

Transform the expression

\frac{1}{u} \times d u = \frac{1}{v} \times d v

Integrate the left-hand side of the equation with respect to u and the right-hand side of the equation with respect to v

\int \frac{1}{u} d u = \int \frac{1}{v} d v

Calculate

More Steps

ln (u) + C_{1} = \int \frac{1}{v} d v, C_{1} \in R

Calculate

More Steps

ln (u) + C_{1} = ln (v) + 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

ln (u) = ln (v) + C, C \in R

Calculate

More Steps

u = e^{C} v, C \in R

Solution

u = C v, C \in R

U = u' v