AP Calculus AB Fun 7 B Verify Solutions to Differential Equations Questions

Practise verification questions by differentiating a proposed function and checking whether it satisfies the given differential equation and conditions.

Exam points

differentiate a proposed function and substitute it into the equation
verify equality and any initial or boundary condition

Given the following differential equation $\frac{dy}{dx}=x-2y+1$ .

For which values of m and b is the line y=m x+b a solution to the differential equation?

m is the slope

$\frac{dy}{dx}$ , so replace into the differential equation: m=x-2(mx+b)+1=(1-2m)x+(1-2b). 1-2m=0 and 1-2b=m, so $m=\frac12$ and $b=\frac14$ .

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AP Calculus AB Fun 7 B Verify Solutions to Differential Equations Questions question 1