Solve a' = u-a - ScanMath

Evaluate

a^{'} = u - a

Rewrite the expression

a^{'} + a = u

Rewrite the expression

a^{'} + 1 \times a = u

Since the equation is written in standard form, determine the functions P (u) and Q (u)

P (u) = 1 Q (u) = u

Insert the function P (u) = 1 into the formula for the integrating factor u (u)

u (u) = e^{\int 1 d u} Q (u) = u

Use the property of integral \int k d x = k x

u (u) = e^{u} Q (u) = u

Insert the integrating factor u (u) and the function Q (u) into the general solution formula

a = \frac{1}{e ^{u}} \times \int u e^{u} d u

Calculate

More Steps

a = \frac{1}{e ^{u}} \times (u e^{u} - e^{u} + C), C \in R

Calculate

a = \frac{u e ^{u} - e ^{u} + C}{e ^{u}}, C \in R

Solution

a = \frac{e ^{u} u - e ^{u} + C}{e ^{u}}, C \in R

Solve the differential equation