In 25-30, find each sum. 10 (_2)kk=l

Math246 Lecture 4: Bernoulli Equations ' t A Bernoulli equation is one of the form y +d (x)y=p x )y t To solve this equation, we will first divide by to get y y+d (x)y1−t=p(x) 1−t Then we substitute w=y and we also take its derivative. Our final equation that we have to solve is 1 ' 1−t w +d (x)w=p(x) Which is in a form we know how to solve. Let’s work on a few examples. Examples 3 y + y=x y4 1. Solve x2 ,y(1)=0 We need to divide everything by y first. −1 '