Solve p' = 2m -p - ScanMath

Evaluate

p^{'} = 2 m - p

Rewrite the expression

p^{'} + p = 2 m

Rewrite the expression

p^{'} + 1 \times p = 2 m

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

P (m) = 1 Q (m) = 2 m

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

u (m) = e^{\int 1 d m} Q (m) = 2 m

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

u (m) = e^{m} Q (m) = 2 m

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

p = \frac{1}{e ^{m}} \times \int 2 m e^{m} d m

Calculate

More Steps

p = \frac{1}{e ^{m}} \times (2 m e^{m} - 2 e^{m} + C), C \in R

Calculate

p = \frac{2 m e ^{m} - 2 e ^{m} + C}{e ^{m}}, C \in R

Solution

p = \frac{2 e ^{m} m - 2 e ^{m} + C}{e ^{m}}, C \in R

P' = 2m P